MathDB

On the equation k+m^k+n^{m^k}}=2009^n - [UKRMO 2009 Grade 8]

Source:

January 21, 2011

number theory proposednumber theory

Problem Statement

а) Prove that for any positive integer

n

there exist a pair of positive integers

(m, k)

such that

{k + m^k + n^{m^k}} = 2009^n.

b) Prove that there are infinitely many positive integers

n

for which there is only one such pair.