Which of the following is true regarding x2≡−1(modp)x^2 \equiv -1 \pmod{p}x2≡−1(modp)?
It always has a solution for any prime ppp
It has a solution if p≡1(mod4)p \equiv 1 \pmod{4}p≡1(mod4)
It has a solution if p≡3(mod4)p \equiv 3 \pmod{4}p≡3(mod4)
It never has a solution