What is a perfect square in mod n

Question

I have been stuck with a question on eliptic curves lately. I need to know whether perfect square mod n is different than a normal perfect square.

And also is 3 a perfect square in mod 13?

Answer 1

Yes, 3 is a perfect square $\bmod 13$ because $4^2 \equiv 16 \equiv 3 \bmod 13.$ All normal squares (i.e. 1,4, 9) less than 13 obviously are perfect squares $\bmod 13$, but as the example 3 shows there are more than these.

Answer 2

$x$ is said to be a perfect square in modulo $n$ if $\exists y$ such that $ y^2\equiv x \pmod{n} $.

And yes, $3$ is a perfect square in$\pmod{13}$ because $4^2\equiv 3\pmod{13}$.