Can someone please revise my proof.
Let $a$ and $x$ be arbitrary integers. Assume $a$ is odd so there exists an integer $k$ s.t $a = 2k + 1$. $a = 2k + 1 = k + k + 1= k + (k+1)$ , evidently $a$ is the sum of two consecutive integers.
Let $a$ be the sum of two consecutive integers. $a = x + (x+ 1) = 2x + 1$. by def. of odd, $a$ must be odd.