cool number theory

Number Theory Level 2

If M and P are positive integers and (M+P)M is even, which of the following must be true?

If M is even,then P is even If M is odd, then P is odd If M is odd, then P is even If M is even, then P is odd All are above true All are above false

1 solution

Alex Delhumeau
May 30, 2015

$(M+P)M = M^2 + PM$ and is even.

If $M$ is odd, then $M^2$ is odd.

If $M^2$ is odd, then $M^2 + PM$ is even if and only if $PM$ is also odd.

If $M$ is odd, then $PM$ is odd if and only if $P$ is odd.

$\implies$ If $M$ is odd, then $P$ is odd.