MathDB

A triple

(a,b,c)

of positive integers is called strong if the following holds: for each integer

m>1

, the number

a+b+c

does not divide

a^m+b^m+c^m

. The sum of a strong triple

(a,b,c)

is defined as

a+b+c

.
Prove that there exists an infinite collection of strong triples, the sums of which are all pairwise coprime.

Problem Statement