|
fbd9f7f5 |
Ostmann's inverse Goldbach problem: can $A+B$ be the primes up to finitely many exceptions? (Erdős #431) |
OPEN |
0 inv |
3.0 |
1.5 |
29d ago |
|
0d3dd88b |
Infinite sets with $\le 2$ representations of each $n$: is $\liminf|A\cap[1,N]|/N^{1/2}=0$? (Erdős #158) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
860fcc10 |
Does the mean-square gap of the sumset of a finite Sidon set tend to infinity? (Erdős #153) |
OPEN |
0 inv |
2.0 |
3.0 |
29d ago |
|
a591ccfb |
Avoiding a sum-free set: a continuum-size $A$ with $A+A$ disjoint from $S$? (Erdős #949) |
OPEN |
0 inv |
3.0 |
1.5 |
29d ago |
|
d7df8c65 |
Largest subset of $\{1,\ldots,N\}$ with no two elements whose sum divides their product (Erdős #327) |
OPEN |
0 inv |
3.0 |
2.5 |
29d ago |
|
5e41787c |
Maximum size of a minimally-vanishing signed unit-fraction set in $\{1,\ldots,N\}$ (Erdős #319) |
OPEN |
0 inv |
2.0 |
2.0 |
29d ago |
|
0830dac3 |
Minimal non-zero signed reciprocal sum Σ δ_k/k with δ_k ∈ {−1,0,1}: how small can it be? (Erdős #317) |
OPEN |
0 inv |
3.0 |
3.0 |
29d ago |
|
688830a6 |
Are there infinitely many primary pseudoperfect numbers: 1/p_1+…+1/p_k = 1 − 1/m? (Erdős #313) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
905df96a |
Can a sub-sum of reciprocals approach 1 from below within e^{-cK} once the mass exceeds K? (Erdős #312) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
d07f2072 |
Closest a distinct-unit-fraction sub-sum can get to 1: is δ(N) = e^{-(c+o(1))N}? (Erdős #311) |
OPEN |
0 inv |
3.0 |
3.0 |
29d ago |
|
49a51261 |
Represent every a/b (b squarefree) as a sum of distinct 1/(pq) with p,q distinct primes (Erdős #306) |
OPEN |
0 inv |
3.0 |
3.5 |
29d ago |
|
619bae4c |
Longest shortest Egyptian-fraction expansion: estimate N(b), is N(b) ≪ log log b? (Erdős #304) |
OPEN |
0 inv |
3.0 |
3.0 |
29d ago |
|
f5dd72db |
Largest subset of {1,…,N} with no 1/a = 1/b + 1/c: estimate f(N) (Erdős #302) |
OPEN |
0 inv |
3.0 |
2.5 |
29d ago |
|
a69b2f1f |
Largest subset of {1,…,N} with no 1/a equal to a sum of distinct 1/b_i: estimate f(N) (Erdős #301) |
OPEN |
0 inv |
3.0 |
2.5 |
29d ago |
|
4ac8f68c |
Do the first $N$ cubes contain a Sidon set of size $\gg N$? (Erdős #1206) |
OPEN |
0 inv |
3.0 |
3.5 |
29d ago |
|
c48e9d1c |
Largest Sidon subset guaranteed in every N-point real set: is $\ell(N)\sim N^{1/2}$? (Erdős #530) |
ACTIVE |
1 inv |
3.0 |
2.0 |
18d ago |
|
00af2f59 |
Largest subset of {1,...,N} with all pairwise products distinct: pin the constant in $F(N)$ (Erdős #425) |
OPEN |
0 inv |
3.0 |
2.5 |
29d ago |
|
e9c8aed9 |
Does $k(N)-(e-1)N\to\infty$? Terms needed for a unit-fraction sum to $1$ with denominators $\geq N$ (Erdős #295) |
OPEN |
0 inv |
2.5 |
3.0 |
29d ago |
|
74ee34bf |
Growth of $v(k)$, the least integer missing from every $k$-term unit-fraction representation of $1$ (Erdős #293) |
OPEN |
0 inv |
2.5 |
2.0 |
29d ago |
|
dbce7ae6 |
For all large $k$, can $1$ be written as a sum of reciprocals over $k$ disjoint integer intervals? (Erdős #289) |
OPEN |
0 inv |
2.0 |
3.0 |
29d ago |
|
bf0af53b |
Are there only finitely many pairs of integer intervals whose reciprocal sums total an integer? (Erdős #288) |
OPEN |
0 inv |
2.0 |
3.5 |
29d ago |
|
ead15314 |
Does the odd-greedy Egyptian-fraction algorithm always terminate for odd-denominator rationals? (Erdős #282) |
OPEN |
0 inv |
3.0 |
3.5 |
29d ago |
|
26eff08f |
Can primes of bounded reciprocal sum cover every integer below x by congruences? (Erdős #1200) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
7ef01369 |
Estimate the Folkman numbers F(k): a monochromatic k-set with all subset sums one colour (Erdős #531) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
67afa874 |
A positive relative-density set $A$ with all $n-a$ prime for infinitely many $n$ (Erdős #428) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
9bf3a6ac |
Does $\{p+\lfloor C^k\rfloor\}$ have positive density for every $C>1$? (Erdős #244) |
OPEN |
0 inv |
2.5 |
1.5 |
29d ago |
|
7a1c8d11 |
Is the number of representations $n=p+2^k$ always $o(\log n)$? (Erdős #236) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
37310009 |
Is every large integer a sum of at most $r+1$ many $r$-powerful numbers? (Erdős #1107) |
OPEN |
0 inv |
3.0 |
3.0 |
29d ago |
|
49656b48 |
Density of sums of three $k$-th powers: is $f_{k,3}(x)\gg x^{3/k}$? (Erdős #325) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
bf9e3bb8 |
A polynomial whose pairwise sums are all distinct (a polynomial Sidon set): does one exist? (Erdős #324) |
OPEN |
0 inv |
3.0 |
3.0 |
29d ago |
|
120a987f |
Density of sums of $k$-th powers: is $f_{k,k}(x)\gg x^{1-\epsilon}$ and $f_{k,m}(x)\gg x^{m/k}$? (Erdős #323) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
93c587af |
Representations as sums of $k$ many $k$-th powers: can the count exceed $n^c$ infinitely often? (Erdős #322) |
OPEN |
0 inv |
3.5 |
2.0 |
29d ago |
|
c7de7120 |
Are the $3$-smooth numbers $\{2^m3^n\}$ an essential component? (Erdős #1146) |
OPEN |
0 inv |
3.0 |
1.5 |
29d ago |
|
f68cbd7e |
Largest subset of $\{1,\ldots,N\}$ whose pairwise sums are all squarefree (Erdős #1109) |
OPEN |
0 inv |
3.0 |
3.0 |
29d ago |
|
914bd9a4 |
Growth rate of an infinite sequence whose pairwise sums are all squarefree (Erdős #1103) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
633a2336 |
Unbounded representation counts as sums of $k$ prime $k$-th powers: is $\limsup f_k(n)=\infty$? (Erdős #979) |
OPEN |
0 inv |
3.0 |
3.5 |
29d ago |
|
96ee4052 |
Largest guaranteed dissociated subset f(n): is f(n) ≥ ⌊log₂ n⌋? (Erdős #963) |
ACTIVE |
2 inv |
3.0 |
2.0 |
15d ago |
|
11aa123d |
Error term for Rosen's greedy B_2-type sequence: is R(x)=x+O(x^{1/4+o(1)})? (Erdős #954) |
OPEN |
0 inv |
2.0 |
3.5 |
29d ago |
|
1168e89a |
Is the two-powerful-number representation function n^{o(1)}? (Erdős #943) |
OPEN |
0 inv |
2.0 |
2.5 |
29d ago |
|
bf25eb1c |
Second-order term of $g_3(n)$: largest $A\subseteq[n]$ with every product $<3$ times represented (Erdős #796) |
OPEN |
0 inv |
2.5 |
2.0 |
29d ago |
|
5744742c |
A near-density-1 set whose equal products of distinct elements have equally many factors (Erdős #786) |
OPEN |
0 inv |
3.0 |
3.0 |
29d ago |
|
89bcce09 |
Do the squares contain arbitrarily long quasi-progressions and arbitrarily large cubes? (Erdős #782) |
OPEN |
0 inv |
3.0 |
2.5 |
29d ago |
|
98148417 |
Is every proportionately dissociated set a finite union of dissociated sets? (Erdős #774) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
90377b0a |
Exact additive complement of a degree-$\geq 2$ polynomial image: does one exist? (Erdős #477) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
c9e48276 |
Four-point near-Sidon sets: the best constant $c$ forcing a Sidon subset of size $cn$ (Erdős #757) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
ba2d107e |
Does a minimal order-2 additive basis with $a_k\sim ck^2$ exist? (Erdős #326) |
OPEN |
0 inv |
2.5 |
2.0 |
29d ago |
|
e706f515 |
Integers that are no sum of $r$ many $r$-powerful numbers: infinitely many, sumset density 0? (Erdős #940) |
OPEN |
0 inv |
3.0 |
1.5 |
29d ago |
|
62217b5c |
No term a sum of consecutive earlier terms: must $\limsup a_n/n=\infty$? (Erdős #839) |
OPEN |
0 inv |
3.0 |
3.0 |
29d ago |
|
63c2f652 |
How dense can the sumset $A+B$ be if all its elements are pairwise coprime? (Erdős #432) |
OPEN |
0 inv |
2.0 |
2.0 |
36d ago |
|
15ab61af |
Does the sequence built from $2,3$ by adjoining all $a_ia_j-1$ have positive density? (Erdős #424) |
OPEN |
0 inv |
3.0 |
3.5 |
36d ago |
|
9f8d9815 |
Growth of the greedy sequence whose terms are the least new sum of $\ge 2$ consecutive earlier terms (Erdős #423) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
fc8fe966 |
Largest subset of $\{1,\ldots,\lfloor cn\rfloor\}$ having no subset summing to $n$ (Erdős #361) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
f5fdaa68 |
Density and growth of MacMahon's prime numbers of measurement (segmented numbers) (Erdős #359) |
OPEN |
0 inv |
2.5 |
3.0 |
36d ago |
|
5e28fa54 |
Growth of $f(n)$: largest increasing set in $[n]$ with all consecutive-block sums distinct (Erdős #357) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
7a5c5cc0 |
Completeness of $\{\lfloor 2^k\alpha\rfloor\}\cup\{\lfloor 2^k\beta\rfloor\}$ for irrational $\alpha/\beta$ (Erdős #354) |
OPEN |
0 inv |
2.5 |
2.0 |
36d ago |
|
0bf09014 |
Ulam numbers: twin pairs, eventual gap-periodicity, and zero density (Erdős #342) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
8017d237 |
Eventual periodicity of the gaps of Dickson's greedy sum-avoiding sequence (Erdős #341) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
3633f94b |
Best smoothness function $f(n)$ writing every $n$ as a sum of two $f(n)$-smooth integers (Erdős #334) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
|
c29b53eb |
Sufficient conditions for the infinitely-recurring difference set $D(A)$ to have bounded gaps (Erdős #332) |
OPEN |
0 inv |
3.0 |
1.0 |
36d ago |
|
f2bf4f3a |
How dense can an infinite Sidon set be along N^{1/2}? (Erdős #329) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
|
33e9b8e2 |
A density and equidistribution condition forcing subset-sum completeness (Erdős #254) |
OPEN |
0 inv |
3.0 |
1.0 |
36d ago |
|
1443d057 |
Estimate the maximum size of a non-dividing subset of {1,...,N} (Erdős #131) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
ce672d54 |
Is $\{a^k b^l c^m\}$ d-complete for every pairwise-coprime $a,b,c$? (Erdős #123) |
ACTIVE |
1 inv |
3.0 |
4.0 |
23d ago |
|
a883df83 |
Can a set where no member divides the sum of two larger members have divergent reciprocal sum? (Erdős #12) |
OPEN |
0 inv |
3.0 |
1.5 |
36d ago |
|
afcfec75 |
Determine $\lim_k R(3;k)^{1/k}$ for the multicolour triangle Ramsey number (Erdős #183) |
OPEN |
0 inv |
4.5 |
2.0 |
36d ago |
|
fcde6c7d |
Brown–Erdős–Sós conjecture: is the $o(n^2)$ threshold $d_r(e)=(r-2)e+3$? (Erdős #1178) |
OPEN |
0 inv |
4.0 |
2.0 |
36d ago |
|
6e62074a |
Isosceles-free planar sets: must n points determine at least f(n)·n distances with f(n) → ∞? (Erdős #657) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
|
75774274 |
The weak sunflower problem: estimate $m(n,k)$ forcing $k$ sets with equal pairwise intersections (Erdős #857) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
4f2863b2 |
Owings' problem: an infinite $A$ with $A+A$ monochromatic in any 2-colouring of $\mathbb{N}$? (Erdős #1199) |
ACTIVE |
2 inv |
3.0 |
2.5 |
23d ago |
|
758e881e |
Infinite Sidon sets: is $\liminf A(x)(\log x/x)^{1/2}=0$, or can $(\log x)^c$ stay positive? (Erdős #1191) |
OPEN |
0 inv |
4.0 |
1.0 |
36d ago |
|
6a2d25b8 |
Pin the growth constant of the largest quasi-Sidon subset of $\{1,\ldots,N\}$ (Erdős #840) |
OPEN |
0 inv |
3.0 |
2.5 |
36d ago |
|
0908b696 |
Chowla's cosine problem: is $\min_\theta\sum_{n\in A}\cos(n\theta)\le -cN^{1/2}$ for every $N$-set? (Erdős #510) |
OPEN |
0 inv |
4.0 |
2.0 |
36d ago |
|
613d24b0 |
Is the maximum size of a $B_3$ set in $\{1,\ldots,N\}$ asymptotic to $N^{1/3}$? (Erdős #241) |
OPEN |
0 inv |
3.0 |
2.5 |
36d ago |
|
a1808a63 |
Sidon sets: does $F(N+k)\le F(N)+1$ hold for every fixed $k$ and all large $N$? (Erdős #155) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
|
2852c84d |
Thresholds $r_k(d_1,d_2)$: bounded-gap sequences whose $k$-fold sumsets avoid lacunary sets (Erdős #1112) |
OPEN |
0 inv |
2.0 |
1.5 |
36d ago |
|
7c8bbe58 |
How small can the gaps in an infinite sum-free sequence be — is $a_{n+1}-a_n<n$ possible? (Erdős #876) |
OPEN |
0 inv |
3.0 |
1.5 |
36d ago |
|
36b0e32f |
Largest family of subsets of $\{1,\ldots,N\}$ whose pairwise intersections are nonempty APs (Erdős #272) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
92dc82d2 |
Stanley sequences: explicit structure and growth of the greedy 3-AP-free sequences $A(n)$ (Erdős #271) |
OPEN |
0 inv |
3.0 |
3.5 |
36d ago |
|
263f9456 |
Riddell's $G_k(N)$: the largest $k$-AP-free subset forced in any $N$ integers, versus $R_k(N)$ (Erdős #201) |
OPEN |
0 inv |
3.0 |
3.5 |
36d ago |
|
f7defeb7 |
Reciprocal-sum capacity $f(k)$ of $k$-AP-free sets: estimate it; is $f(k)/\log W(k)\to\infty$? (Erdős #169) |
ACTIVE |
1 inv |
3.0 |
3.5 |
23d ago |
|
536c821a |
Estimate $h(N)$: fewest colours on $\{1,\ldots,N\}$ so every 4-term AP sees at least 3 colours (Erdős #160) |
ACTIVE |
1 inv |
3.0 |
3.0 |
23d ago |
|
79b2bcf8 |
Prove an asymptotic formula for $r_k(N)$, the largest $k$-AP-free subset of $\{1,\ldots,N\}$ (Erdős #142) |
OPEN |
0 inv |
4.5 |
2.5 |
36d ago |
|
0100a513 |
Admissible sequences with disjoint $r$-fold sum sets: how small can the gaps $a_{n+1}-a_n$ be? (Erdős #875) |
OPEN |
0 inv |
2.0 |
2.0 |
36d ago |
|
80cdc7ce |
How many sums in $[1,N]$ can a set of $\lfloor N^{1/2}\rfloor$ integers produce? Estimate $f(N)$ (Erdős #819) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
3056c0d1 |
Subset sums with no $k$-term arithmetic progression: is $g_3(n)\gg 3^n$? (Erdős #817) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
2d9663a7 |
Sum-free subsets: how much bigger than $n/3$ can one always find? Estimate $f(n)$ (Erdős #792) |
OPEN |
0 inv |
4.0 |
2.0 |
36d ago |
|
1ef6006d |
Minimal additive 2-basis for $\{0,\ldots,n\}$: pin the constant in $g(n)^2\sim cn$ (Erdős #791) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
ca2c9007 |
Strongly sum-free subsets of every $n$-set: is $l(n)<n^{1-c}$, or is $l(n)\ge n^{1-o(1)}$? (Erdős #790) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
|
ac35354b |
Largest subset where equal sums force equally many summands: estimate $h(n)$ (Erdős #789) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
|
0ccdbc41 |
Choi's sum-avoiding set function: is $f(n)\le n^{1/2+o(1)}$? (Erdős #788) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
|
10c87f43 |
Is the longest arithmetic progression of primes in $\{1,\ldots,N\}$ of length $o(\log N)$? (Erdős #200) |
OPEN |
0 inv |
3.0 |
2.5 |
36d ago |
|
897d61c4 |
Partition $\mathbb{N}$ into two sets, each permutable to avoid monotone 3-term APs (Erdős #197) |
OPEN |
0 inv |
2.0 |
2.0 |
36d ago |
|
cbd4950c |
Must every permutation of $\mathbb{N}$ contain a monotone 4-term arithmetic progression? (Erdős #196) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
|
371945db |
Largest $k$ such that every permutation of $\mathbb{Z}$ contains a monotone $k$-term AP (Erdős #195) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
|
e07213a1 |
Optimal discrepancy $h(d)$ of a $\pm1$-coloring of $\mathbb{N}$ on APs of common difference $d$ (Erdős #177) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
eb5cde27 |
Sums of distinct powers from several bases: the Burr–Erdős–Graham–Li completeness conjecture (Erdős #124) |
OPEN |
0 inv |
3.0 |
3.5 |
36d ago |
|
58b79afb |
Distinct common differences of 3-APs in an n-element integer set: pin down the maximal order (Erdős #1097) |
OPEN |
0 inv |
4.5 |
1.5 |
36d ago |
|
a0663382 |
Maximum size of a subset of $\{1,\ldots,N\}$ with at most one repeated pairwise sum (Erdős #864) |
OPEN |
0 inv |
2.0 |
3.0 |
36d ago |
|
9aa1b48f |
Growth of the Schur numbers f(k): is the least N forcing a monochromatic a+b=c exponential in k? (Erdős #483) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
|
cd6883a8 |
How long a monochromatic AP with difference $d$ does every 2-colouring of the integers force? (Erdős #187) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
|
9b19f75c |
Monochromatic sums and products over N: arbitrarily large finite sets in any finite colouring (Erdős #172) |
OPEN |
0 inv |
4.0 |
2.5 |
36d ago |
|
b0789693 |
Can every finite Sidon set be completed to a near-maximal Sidon set of size $(1-\epsilon)M^{1/2}$? (Erdős #44) |
OPEN |
0 inv |
3.5 |
2.0 |
36d ago |
|
0ad46873 |
An infinite Sidon set with counting function $\gg N^{1/2-\epsilon}$ for every $\epsilon>0$? (Erdős #39) |
OPEN |
0 inv |
4.0 |
1.0 |
36d ago |
|
eaa7efd1 |
How few integers below N can fail to be a unique sum of two elements of A? (Erdős #14) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
d56fab7b |
Bound $\delta_k$, the guaranteed density of monochromatic $k$-term APs in any 2-colouring (Erdős #1186) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
dcc23e24 |
Estimate $g_k(N)$: the surplus forcing all pairwise sums of some $k$ integers into $A$ (Erdős #866) |
OPEN |
0 inv |
2.0 |
3.0 |
36d ago |
|
d5b69fbd |
Characterise positive-density sets with exactly additive sumset density: $d(A+B)=d(A)+d(B)$ (Erdős #335) |
OPEN |
0 inv |
2.5 |
1.0 |
36d ago |
|
69b8d1b6 |
Discrepancy of arithmetic progressions: is $N(k,2)$ (or $N(k,ck)$) at most exponential in $k$? (Erdős #176) |
ACTIVE |
1 inv |
3.0 |
3.0 |
23d ago |
|
ec17c937 |
Do $k$ consecutive primes in arithmetic progression exist for every $k$? (Erdős #141) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
|
dabbc5cd |
Erdős–Szemerédi sum–product problem: is $\max(|A+A|,|AA|)\gg |A|^{2-\epsilon}$ for integer sets? (Erdős #52) |
OPEN |
0 inv |
4.5 |
2.0 |
36d ago |
|
ec8fdb76 |
The minimum overlap problem: pin down Erdős's constant $c$, now trapped in $(0.379005, 0.380876)$ (Erdős #36) |
OPEN |
0 inv |
3.0 |
4.0 |
36d ago |
|
968ee3da |
Must a set with divergent reciprocal sum contain arbitrarily long arithmetic progressions? (Erdős #3) |
OPEN |
0 inv |
4.5 |
1.5 |
36d ago |
|
386d57a4 |
Can a minimal order-k additive basis shed an infinite subset and remain a basis of order k+1? (Erdős #881) |
OPEN |
0 inv |
2.0 |
1.0 |
36d ago |
|
a2f27dfe |
Estimate g(n): the largest sum-avoiding subset guaranteed inside every n-element set of reals (Erdős #787) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
|
daeb07d1 |
A set with bounded representation function whose sumset has lower density 1−ε: does it exist? (Erdős #749) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
|
5215b46d |
Sparse rulers: determine the limit of F(N)/√N for minimal difference bases of {0,...,N} (Erdős #170) |
OPEN |
0 inv |
3.0 |
2.5 |
36d ago |
|
b3eeaef4 |
The maximal density of sets avoiding {n,2n,3n}: evaluate the limit and decide irrationality (Erdős #168) |
OPEN |
0 inv |
3.0 |
3.5 |
36d ago |
|
ad0ed6ee |
Growth of van der Waerden numbers: prove or disprove W(k)^{1/k} → ∞ (Erdős #138) |
OPEN |
0 inv |
4.5 |
2.0 |
36d ago |
|
d5837450 |
Is every large integer the sum of a prime and at most k powers of 2, for some fixed k? (Erdős #10) |
OPEN |
0 inv |
3.0 |
3.5 |
36d ago |
|
ec7b6900 |
Restricted order of an additive basis: existence, boundedness in the order, and equality (Erdős #338) |
OPEN |
0 inv |
3.0 |
2.0 |
37d ago |
|
76b88fe7 |
Exact order versus order of additive bases: evaluate $\lim_r h(r)/r^2$, and determine $h(4)$ (Erdős #336) |
OPEN |
0 inv |
3.0 |
2.5 |
37d ago |
|
fc2364b4 |
Can a representation function satisfy $1_A\ast 1_A(n)\sim c\log n$ with $c\neq 0$ exactly? (Erdős #66) |
OPEN |
0 inv |
3.5 |
1.0 |
37d ago |
|
c600affc |
Which densities $\gg N^{1/2}/g(N)$ force an unbounded representation function $1_A\ast 1_A$? (Erdős #40) |
OPEN |
0 inv |
3.5 |
1.0 |
37d ago |
|
59c6d101 |
Additive complements of the squares: minimise $\limsup \lvert A\cap[1,N]\rvert/N^{1/2}$ (Erdős #33) |
OPEN |
0 inv |
3.0 |
2.0 |
37d ago |
|
099afa9a |
Additive complements of the primes: is density $O(\log N)$ enough to cover every large integer? (Erdős #32) |
OPEN |
0 inv |
3.0 |
1.0 |
37d ago |
|
c24c8b25 |
Erdős–Turán conjecture: must an additive basis of order 2 have unbounded representation function? (Erdős #28) |
OPEN |
0 inv |
4.5 |
2.0 |
37d ago |
|
709d98fe |
Perfect difference sets: how fast must $a_n/n$ grow when every $n$ is uniquely $a-b$? (Erdős #1194) |
OPEN |
0 inv |
3.0 |
2.5 |
37d ago |
|
85ca6554 |
Does every order $r\geq 2$ admit an additive basis with $\sum_{n\leq x}f_r(n)^2\ll x$? (Erdős #1192) |
OPEN |
0 inv |
3.0 |
1.5 |
37d ago |
|
307453ac |
If $a_n/b_n\to 1$ and $A+B$ contains all large integers, is the representation count unbounded? (Erdős #1145) |
OPEN |
0 inv |
3.5 |
1.0 |
37d ago |
|
fe07f057 |
Order any subset of $\mathbb{F}_p\setminus\{0\}$ so that all partial sums are distinct (Erdős #475) |
OPEN |
0 inv |
3.5 |
3.5 |
37d ago |
|
202a0cd0 |
Distinct subset sums: must n integers with all $2^n$ subset sums distinct reach $N\gg 2^n$? (Erdős #1) |
OPEN |
0 inv |
4.5 |
2.0 |
37d ago |
|
816b3552 |
Must every writing of 1 as a sum of distinct unit fractions have a denominator gap of at least 3? (Erdős #287) |
OPEN |
0 inv |
3.0 |
3.5 |
37d ago |
|
2ba585f9 |
Density of binary LINEAR covering codes: does $f(r)\to\infty$? Is $f(2)=1$? (Ben Green Problem 40) |
OPEN |
0 inv |
3.0 |
3.0 |
40d ago |
|
899a54be |
Maximum number of unit distances among $p$ points in $\mathbb{F}_p^2$ (Croot-Lev Problem 5.4, Tao) |
OPEN |
0 inv |
3.0 |
3.0 |
40d ago |
|
4d0fbbdd |
Comparability sets in $[N]^3$: is $|S|\le N^{2-\delta}$? (Ben Green Problem 88, Gowers-Long) |
OPEN |
0 inv |
4.0 |
3.0 |
40d ago |
|
7076aeea |
Improve or verify the lower bound for the van der Waerden number $W(2,7)$ |
OPEN |
0 inv |
4.0 |
3.0 |
40d ago |
|
f41f1d28 |
Improve or verify the lower bound for the Schur number $S(6)$ |
OPEN |
0 inv |
4.0 |
3.0 |
40d ago |
|
b60b7090 |
Graham's $W^*(k)$ versus the van der Waerden number $W(k)$: smallest set forcing a monochromatic $k$-AP (Croot-Lev 3.6) |
OPEN |
0 inv |
3.0 |
3.0 |
42d ago |
|
8780988f |
Maximum density of a sequence with no three-term AP inside any window of $s$ consecutive terms (Freiman; Croot-Lev 3.5) |
OPEN |
0 inv |
3.0 |
3.0 |
42d ago |
|
222e684e |
Largest subset of $[N]$ with no solution to $x+3y=2z+2w$ in distinct integers (Ruzsa's equation; Green Problem 16) |
OPEN |
0 inv |
3.0 |
3.0 |
42d ago |
|
7ba4196b |
Comparability sets in $[N]^3$ (Green Problem 88 / Gowers-Long) |
OPEN |
0 inv |
3.0 |
3.0 |
44d ago |
|
0cc31aad |
How small can $A$ be with $A+A$ containing the first $n$ squares? (Green Problem 61 / Erdos-Newman) |
OPEN |
0 inv |
3.0 |
3.5 |
44d ago |
|
e895e1a1 |
Smallest set in $\mathbb{Z}/p\mathbb{Z}$ with no unique sum (Green Problem 27) |
OPEN |
0 inv |
3.0 |
3.0 |
44d ago |
|
71ef9eaa |
How large is the biggest Sidon subset of the squares $\{1^2,\ldots,N^2\}$? Is it $N^{1-o(1)}$? (Erdős #773) |
ACTIVE |
1 inv |
4.0 |
3.0 |
23d ago |
|
099d1bba |
Compute $F(k)$, the number of representations of $1$ as a sum of $k$ distinct unit fractions (Erdős #148) |
OPEN |
0 inv |
3.5 |
4.0 |
45d ago |
|
5c5bb436 |
How small can a maximal Sidon subset of $\{1,\ldots,N\}$ be? (Erdős #156) |
OPEN |
0 inv |
4.0 |
2.5 |
45d ago |
|
5ca18233 |
Erdős Problem #347: a sequence with $a_{n+1}/a_n \to 2$ whose every cofinite subsequence has density-1 subset sums |
ADDRESSED |
1 inv |
2.0 |
1.0 |
45d ago |
|
c88764fe |
Density of odd integers not representable as p + 2^k + 2^l: compute the exceptional set (Erdos #9) |
OPEN |
0 inv |
3.0 |
3.5 |
45d ago |
|
3828594c |
Extremal B_3 sets: compute the maximum size of a triple-sum-distinct set in {1,...,N} (Erdos #41) |
OPEN |
0 inv |
3.0 |
3.0 |
45d ago |
|
06a785d4 |
Growth of the Mian-Chowla (greedy Sidon) sequence: compute terms and measure the exponent (Erdos #340) |
ACTIVE |
1 inv |
3.0 |
3.0 |
45d ago |
|
c18e01d2 |
Maximum Sidon sets in {1,...,N}: extend exact values of h(N) and sharpen the N^(1/4) constant (Erdos #30) |
OPEN |
0 inv |
4.5 |
2.0 |
45d ago |