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This research aims to determine the exact maximum cardinality of a specific subset under given conditions.

August 8, 2026Open Access

Erdős Problem 848: A Kernel-Checked Proof of the Exact Extremal Bound

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This research aims to determine the exact maximum cardinality of a specific subset under given conditions.
Applied Hall reformulation to demonstrate extremal bounds.
Utilized exact prefix colourings for N ≤ 5·10^6.
Employed square-divisor estimates and quadratic equation transformations for larger N.
Proved |A| ≤ floor((N+18)/25) with equality for elements congruent to 7 modulo 25.
Closed the finite range left by previous asymptotic results.
Established required inequalities through semantic checkers and Lean 4 kernel validation.

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Randomized trial establishes exact maximum cardinality in subset conditions, indicating precise extremal value.

Alex Chengyu Li (2026) studied this question.

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