MathDB

N10

Part of 2021-IMOC

Problems(1)

IMOC 2021 N10

Source: IMOC 2021 N10

8/11/2021
A prime is called perfect if there is a permutation a1,a2,⋯ ,ap−12,b1,b2,⋯ ,bp−12a_1, a_2, \cdots, a_{\frac{p-1}{2}}, b_1, b_2, \cdots, b_{\frac{p-1}{2}} of 1,2,⋯ ,p−11, 2, \cdots, p-1 satisfies bi≡ai+1ai(modp)b_i \equiv a_i + \frac{1}{a_i} \pmod p for all 1≤i≤p−121 \le i \le \frac{p-1}{2}. Show that there are infinitely many primes that are not perfect.
Proposed By - CSJL
number theoryIMOC