# number theory – Let a ≡ 1 mod (4) and p an odd prime. Show that the Legendre symbol (a/p) only depends on p mod (a)

Let $$a equiv 1 pmod 4$$ and let $$p$$ be an odd prime. Show that $$left( frac{a}{p}right)$$ only depends on $$p pmod a$$.

I know that $$left(frac{a}{p}right)=left(frac{p}{a}right)$$ because of the law of quadratic reciprocity. But I don’t know how to go on.

Can I use Euler’s criterion to prove this?