MathDB

For every pair of positive integers

(n,m)

with

n<m

, denote

s(n,m)

be the number of positive integers such that the number is in the range

[n,m]

and the number is coprime with

m

. Find all positive integers

m\ge 2

such that

m

satisfy these condition: i)

\frac{s(n,m)}{m-n} \ge \frac{s(1,m)}{m}

for all

n=1,2,...,m-1

; ii)

2022^m+1

is divisible by

m^2

Problem Statement