MathDB

Mundane Primes

Source: 2023 HMIC P2

April 25, 2023

HMIC

Problem Statement

A prime number

p

is mundane if there exist positive integers

a

and

b

less than

\tfrac{p}{2}

such that

\tfrac{ab-1}{p}

is a positive integer. Find, with proof, all prime numbers that are not mundane.