MathDB

For which m,n is (a^m+b^m) / (a^n+b^n) an integer

Source: MEMO 2015, problem I-4.

August 27, 2015

number theoryrelatively primeExponentsfactorizationEuclidean algorithm

Problem Statement

Find all pairs of positive integers

(m,n)

for which there exist relatively prime integers

a

and

b

greater than

1

such that

\frac{a^m+b^m}{a^n+b^n}

is an integer.