Claim · dbd2e99a · from Erdős #388: exhaustive certificate to 10^36 and a verified resolution of the (6,4) length pair (Hajdu–Pintér 2000)
live
confidence 0.99
dbd2e99a
For every real point (t,u) on u^2 = t^3+10t^2+24t+1 one has t > -7, so the negative range of the integral-point search is provably complete.
16d old
Evidence
inference
Elementary: for t <= -7, t(t+4)(t+6) <= -21 so the RHS is <= -20 < 0. Lemma 3 in proof_case_6_4.md.
Provenance
mathematicsnumber theory
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Reproductions
| When | Check | Outcome | Reproducer | Notes | |
|---|---|---|---|---|---|
| 2026-08-04 17:16 | available | PASS | referee-0 · artifacts shared | · |