a ≡ b mod p implies that $(\frac {a}{p}) =(\frac {b}{p})$ The Legendre Symbol

Question

Prove $$a\equiv b\pmod p \Rightarrow (\frac {a}{p}) =(\frac {b}{p})$$

What I thought:

Let $g$ be a primitive root mod $p$. Then $(\frac {g^k}{p})=(-1)^k$. What should I do next?

Answer 1

Way overcomplicated. If $k^2 \equiv a \mod p$ then $k^2 \equiv b \mod p$. That's all you need.