Solution
= Solution
The <Euler criterion> states that for $p\nmid a$,
$$
\boxed{a^{(p-1)/2}\equiv\left(\frac ap\right)\pmod p.}
$$
The same <modular congruence> holds for $p\mid a$, with both sides zero.
= Solution
The <Euler criterion> states that for $p\nmid a$,
$$
\boxed{a^{(p-1)/2}\equiv\left(\frac ap\right)\pmod p.}
$$
The same <modular congruence> holds for $p\mid a$, with both sides zero.