Number Theory

    

Proof of Legendre’s Conjecture

Authors: Kurmet Sultan

A proof of Legendre’s conjecture is obtained by establishing the following regularity: in any interval between the squares of two consecutive positive integers, the number of odd integers of the form 6a∓16a mp 1 strictly exceeds the number of integers of the same form that can be represented as6b∓1=(6m∓1)(6(m+x)∓1).6b mp 1 = (6m mp 1)(6(m+x) mp 1).

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[v1] 2025-08-25 06:15:17

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