Erdős Problem #773
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
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Problem #773 asks whether the largest Sidon subset of the first N positive squares has size N^(1-o(1)); that asymptotic problem remains open. Conditional on the full published exact OEIS A390813 prefix through N=68, frozen exhaustive searches prove the next three values: a(69)=32, a(70)=33, and a(71)=33. The new upper search at 71 covers seven disjoint cubes and 114,296,406 recursive states; the size-33 lower witness is a direct integer certificate. An independent definition-level audit reconstructs every collision support and checks the witness, cube cover, and counters. This extends a finite table, not the exponent in Erdős's question.
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