MathDB

JBMO Shortlist 2022 N5

Source: JBMO Shortlist 2022

June 26, 2023

number theoryremainderprimeJuniorBalkanshortlist

Problem Statement

Find all pairs

(a, p)

of positive integers, where

p

is a prime, such that for any pair of positive integers

m

and

n

the remainder obtained when

a^{2^n}

is divided by

p^n

is non-zero and equals the remainder obtained when

a^{2^m}

is divided by

p^m