Number Theory

    

The Proofs of Legendre’s Conjecture and Three Related Conjectures

Authors: Wing K. Yu

In this paper, we are going to prove Legendre’s Conjecture: There is a prime number between n^2 and (n+1)^2 for every positive integer n. We will also prove three related conjectures. The method that we use is to analyze a binomial coefficient. It has been developed from the method of analyzing a central binomial coefficient that was used by Paul Erdős to prove Bertrand’s postulate - Chebyshev’s theorem.

Comments: 11 Pages.

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Submission history

[v1] 2022-06-07 13:00:55
[v2] 2022-06-28 00:14:40
[v3] 2022-11-27 18:05:11
[v4] 2022-12-12 06:06:11
[v5] 2023-02-24 06:23:30

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