MathDB

1

Part of 2016 Serbia National Math Olympiad

Problems(1)

Exist big m such that...

Source: Serbia Math Olympiad 2016 P1

4/1/2016
Let n>1n>1 be an integer. Prove that there exist m>nnm>n^n such that nm−mnm+n\frac {n^m-m^n}{m+n} is a positive integer.
number theorySerbiaDivisibility