%0 Journal Article
%T A Method for Solving Legendre's Conjecture
%A Hashem Sazegar
%J Journal of Mathematics Research
%D 2012
%I 
%R 10.5539/jmr.v4n1p121
%X Legendre's conjecture states that there is a prime number between $n^2$ and $(n+1)^2$ for every positive integer $n$. In this paper we prove that every composite number between $n^2$ and $(n+1)^2$ can be written $u^2-v^2$ or $u^2-v^2+u-v$ that $u>0$ and $vgeq 0$. Using these result as well as induction and residues $(modq)$ we prove Legendre's conjecture.
%U http://www.ccsenet.org/journal/index.php/jmr/article/view/12401