Prove $a = 2 \cdot 10^{2016} + 16$ cannot be a perfect square 
Prove the number $a = 2 \cdot 10^{2016} + 16$ cannot be a perfect square.

I tried studying $a \mod b$ for different integers $b$, without succes.

Note that we have
$$
2\cdot 10^{2016} + 16 \equiv 2\cdot(-1)^{2016} + 5 = 7\pmod {11}
$$
but the only squares modulo $11$ are $0, 1, 3, 4, 5, 9$.
