MathDB

GCD Isn't 1

Source: 2021 AIME II #9

March 19, 2021

number theorygreatest common divisorAMCAIMEAIME II

Problem Statement

Find the number of ordered pairs

(m, n)

such that

m

and

n

are positive integers in the set

\{1, 2, ..., 30\}

and the greatest common divisor of

2^m + 1

and

2^n - 1

is not

1.