Proof:
Suppose ## N ## is the integer and ## x ## is the units digit of ## N ##.
Then ## N=10k+x ## for some ## k\in\mathbb{Z} ## where ## x={0, 1, 2, 3, 4, 5, 6, 7, 8, 9} ##.
Note that ## 10k\equiv 0\pmod {2}\implies N\equiv x\pmod {2} ##.
Thus ## 2\mid N\implies N\equiv 0\pmod {2}\implies...