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Aigner, M. and Ziegler, G.M. (2014) Proofs from THE BOOK. 5th Edition, Chapter 2, Springer, Berlin.

has been cited by the following article:

• TITLE: The Proofs of Legendre’s Conjecture and Three Related Conjectures

  AUTHORS: Wing K. Yu

  KEYWORDS: Legendre’s Conjecture, Bertrand’s Postulate - Chebyshev’s Theorem, Oppermann’s Conjecture, Brocard’s Conjecture, Andrica’s Conjecture

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.11 No.5, May 23, 2023

  ABSTRACT: In this paper, we prove Legendre’s conjecture: There is a prime number between n2 and (n +1)2 for every positive integer n. We also prove three related conjectures. The method that we use is to analyze binomial coefficients. It is developed by the author from the method of analyzing binomial central coefficients, that was used by Paul Erdős in his proof of Bertrand’s postulate - Chebyshev’s theorem.