MathDB

A prime is called perfect if there is a permutation

a_1, a_2, \cdots, a_{\frac{p-1}{2}}, b_1, b_2, \cdots, b_{\frac{p-1}{2}}

1, 2, \cdots, p-1

satisfies

b_i \equiv a_i + \frac{1}{a_i} \pmod p

for all

1 \le i \le \frac{p-1}{2}

. Show that there are infinitely many primes that are not perfect.
Proposed By - CSJL

Problem Statement