Unusual syntax for finite field

Question

I found in an exercise the following syntax: Polynomial f(x) =..... is a polynomial in Fp with p = 2 mod 5 or p =3 mod 5. I have to show that it is irreducible.

I don't know this Syntax p= 2 mode 5 for a field. Does anybody know the meaning ?

Answer 1

This just means a $p$ such that $p \equiv 2 \pmod 5$. For example 7 or 17 are such numbers which happen to be primes. However, note that $p$ is not necessarily a prime, so I would suggest writing $q$ instead of $p$ (or maybe $p$ is assumed to be a prime in your case).