Prove that there exists exactly 1 solution to $x^2 \equiv a \pmod{2}$ where $a \in \mathbb{Z}$.

Question

Prove that there exists exactly 1 solution to $x^2 \equiv a \pmod{2}$ where $a \in \mathbb{Z}$.

I've been looking around for this problem, but I haven't found it here so I asked. What the title says. Thank you in advance for anyone who takes their time to help me :)

Answer 1

Note $x^2\equiv x\pmod{2}$ so $x\equiv a \pmod{2}$ is the only solution.