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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 |
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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 |
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89bcce09 |
Do the squares contain arbitrarily long quasi-progressions and arbitrarily large cubes? (Erdős #782) |
OPEN |
0 inv |
3.0 |
2.5 |
29d ago |
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98148417 |
Is every proportionately dissociated set a finite union of dissociated sets? (Erdős #774) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
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f3d8a75e |
Density and liminf of $h(n)$, least $l$ making $2^n\!-\!1,\ldots,l^n\!-\!1$ pairwise coprime (Erdős #770) |
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0 inv |
2.5 |
2.5 |
29d ago |
|
5f9b6ec8 |
Restricted Mertens sum over primes with $n\bmod p\in(p/2,p)$: is it $\sim\tfrac12\log\log n$? (Erdős #726) |
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0 inv |
2.5 |
2.0 |
29d ago |
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f0166e1d |
Bound $f(n,m)$ for distinct multiples $k\mid a_k$: is $\max_m f(n,m)\le n^{1+o(1)}$? (Erdős #711) |
OPEN |
0 inv |
3.0 |
3.0 |
29d ago |
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7ec2e726 |
Distinctness of consecutive-block lcms: is $M(n,k)\neq M(m,k)$ whenever $m\ge n+k$? (Erdős #677) |
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0 inv |
2.5 |
3.0 |
29d ago |
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51143567 |
Is every large integer of the form $ap^2+b$ with $p$ prime, $a\ge1$, $0\le b<p$? (Erdős #676) |
OPEN |
0 inv |
3.0 |
3.5 |
29d ago |
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00d54a95 |
Translation property: sums of two squares, prime-restricted sets, and squarefree shift growth (Erdős #675) |
OPEN |
0 inv |
2.5 |
2.5 |
29d ago |
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9f279e68 |
Least prime missing from a product of $k$ consecutive integers: is $q(n,k)<(1+o(1))\log n$? (Erdős #663) |
OPEN |
0 inv |
2.0 |
2.0 |
29d ago |
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5ccf31c6 |
Estimate $h(n)$: fewest distinct ratios $a/\gcd(a,b)$ forced by an $n$-element set (Erdős #539) |
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0 inv |
3.0 |
2.5 |
29d ago |
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52d0e6a5 |
Best-possible upper bound for $\sum_{n\in A}1/n$ under an at-most-$r$ prime-representation cap (Erdős #538) |
OPEN |
0 inv |
2.0 |
2.0 |
29d ago |
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d74129a9 |
Estimate $f_r(N)$: largest subset of $\{1,\ldots,N\}$ with no $r$ elements sharing one pairwise gcd (Erdős #535) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
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b6667243 |
Second moment of gaps among non-multiples of a sparse set: does the limit exist? (Erdős #489) |
OPEN |
0 inv |
2.5 |
2.0 |
29d ago |
|
9fbc536c |
Graham's conjecture: for every $k\neq 1$, infinitely many $n$ with $2^n\equiv k\pmod{n}$? (Erdős #479) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
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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 |
|
3aa15e1f |
Ulam's greedy prime sequence $q_{n+1}=$ least prime $q_n+q_i-1$: can it be infinite? (Erdős #472) |
OPEN |
0 inv |
2.5 |
3.0 |
29d ago |
|
4f9fad7b |
Two-part prime congruence cover: split $\{p\leq x\}$ so every $n<x$ is hit in both parts (Erdős #467) |
OPEN |
0 inv |
2.0 |
2.0 |
29d ago |
|
1e833fbd |
Divergence of $\sum 1/a_i$ for the Eggleton–Erdős–Selfridge coprime sequence (Erdős #460) |
OPEN |
0 inv |
2.5 |
2.5 |
29d ago |
|
964173a6 |
Smallest prime $\equiv 1\ (\mathrm{mod}\ n)$ versus smallest $m$ with $n\mid\phi(m)$ (Erdős #456) |
OPEN |
0 inv |
2.5 |
2.5 |
29d ago |
|
933a3949 |
Convex-gap prime sequences: must $q_n/n^2\to\infty$? (Erdős #455) |
OPEN |
0 inv |
3.0 |
1.5 |
29d ago |
|
708a7e90 |
Longest run in $[x,2x]$ of integers with more than $\log\log n$ distinct prime factors (Erdős #452) |
OPEN |
0 inv |
3.0 |
3.5 |
29d ago |
|
84d66419 |
Distinct-distance subsets: estimate the guaranteed size $F_d(n)$ in any $n$ points of $\mathbb{R}^d$ (Erdős #1208) |
OPEN |
0 inv |
3.0 |
2.5 |
29d ago |
|
4876423e |
Factor-difference sets: do $k$ integers always share $\geq k$ common factor differences? (Erdős #885) |
OPEN |
0 inv |
3.0 |
2.5 |
29d ago |
|
11a9e739 |
Density $d_t$ of $n$ representing $t$ as a sum of distinct divisors: is $d_t\sim c_1(\log t)^{-c_2}$? (Erdős #859) |
OPEN |
0 inv |
2.0 |
2.5 |
29d ago |
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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 |
|
85a4a384 |
Intervals nearly free of integers with a divisor in $(n,2n)$: how large must $y(\epsilon,n)$ be? (Erdős #450) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
0627383b |
Practical numbers with tiny representations: is $h(m)<(\log\log m)^{O(1)}$ infinitely often? (Erdős #18) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
88bbdc31 |
Lagrange interpolation at Chebyshev nodes: realise every closed set as its limit points (Erdős #1151) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
dfd2930b |
Node sets forcing every low-degree near-interpolant to exceed a fixed bound (Erdős #1133) |
OPEN |
0 inv |
3.0 |
1.5 |
29d ago |
|
04244230 |
Largest measure of a bounded planar set with no two points an integer distance apart (Erdős #953) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
dae93785 |
Distinct distances under a no-three-concyclic-per-centre condition: at least $(1+c)n/2$? (Erdős #655) |
OPEN |
0 inv |
2.5 |
2.0 |
29d ago |
|
bacde559 |
Cochromatic gap of the random graph: is $\chi(G)-\zeta(G)\to\infty$ almost surely? (Erdős #625) |
OPEN |
0 inv |
4.0 |
1.0 |
29d ago |
|
9e1b354e |
Is the largest disc inside $\{|f|<1\}$ of radius $\gg 1/n$ for roots in the unit disc? (Erdős #1039) |
OPEN |
0 inv |
3.0 |
2.5 |
29d ago |
|
9de66620 |
An entire function whose every derivative-subsequence has dense zero set: does one exist? (Erdős #906) |
OPEN |
0 inv |
2.0 |
1.0 |
29d ago |
|
5724ea9e |
Can Lagrange interpolation converge while the Lebesgue function diverges? (Erdős #671) |
OPEN |
0 inv |
3.0 |
1.5 |
29d ago |
|
a5d64348 |
Bound the length of a path along which an entire function outgrows every power $z^n$ (Erdős #514) |
OPEN |
0 inv |
2.0 |
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 |
|
ab8cc421 |
Estimate $h(n)$, the powerful integers in $[n^2,(n+1)^2)$: is it $(\log n)^{c+o(1)}$? (Erdős #942) |
OPEN |
0 inv |
3.0 |
2.5 |
29d ago |
|
e706f515 |
Integers that are no sum of $r$ many $r$-powerful numbers: infinitely many, sumset density 0? (Erdős #940) |
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0 inv |
3.0 |
1.5 |
29d ago |
|
063b8c26 |
Can a sum of $r-2$ coprime $r$-powerful numbers be $r$-powerful (open case $r=4$)? (Erdős #939) |
OPEN |
0 inv |
3.0 |
3.0 |
29d ago |
|
e7603de8 |
Finitely many 3-term arithmetic progressions among consecutive powerful numbers? (Erdős #938) |
OPEN |
0 inv |
2.5 |
3.0 |
29d ago |
|
17de0d4c |
Are $2^n\pm1$ and $n!\pm1$ powerful for only finitely many $n$? (Erdős #936) |
OPEN |
0 inv |
3.0 |
2.5 |
29d ago |
|
55e3d2b6 |
Is the $\{2,3\}$-part of $n(n+1)$ infinitely often much larger than $n\log n$? (Erdős #933) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
c9854261 |
Two integers between consecutive primes with all prime factors below the gap, infinitely often (Erdős #932) |
OPEN |
0 inv |
2.5 |
3.0 |
29d ago |
|
901abe42 |
Products of consecutive integers over disjoint long intervals: never a perfect power? (Erdős #930) |
OPEN |
0 inv |
3.5 |
1.5 |
29d ago |
|
4b854247 |
Gaps between totatives of a primorial: which even numbers occur, and how often? (Erdős #854) |
OPEN |
0 inv |
2.5 |
4.0 |
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 |
|
89323dcf |
Are there infinitely many amicable pairs, and is $A(x)>x^{1-o(1)}$? (Erdős #830) |
OPEN |
0 inv |
3.0 |
2.5 |
29d ago |