MathNet 2013 Question 53

Given a prime $p \ge 5$, show that there exist at least two distinct primes $q$ and $r$ in the range $2, 3, \dots, p-2$ such that $q^{p-1} \not\equiv 1 \pmod{p^2}$ and $r^{p-1} \not\equiv 1 \pmod{p^2}$.