suppose 'n' is a positive integer and (2n+1) is the square of an integer. show that (n+1) is the sum of squares of two integers
Follow Math Help Forum on Facebook and Google+
$\displaystyle 2n+1=k^2$ The left side is an odd number, so $\displaystyle k=2p+1$. Then $\displaystyle 2n+1=4p^2+4p+1\Rightarrow n=2p^2+2p\Rightarrow n+1=2p^2+2p+1=p^2+(p+1)^2$
View Tag Cloud