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3^m = 2^k + 7^n and geometric series

Source: 2012 Indonesia Round 2 TST 4 Problem 4

March 18, 2012
number theory unsolvednumber theory

Problem Statement

Find all quadruplets of positive integers (m,n,k,l)(m,n,k,l) such that 3m=2k+7n3^m = 2^k + 7^n and mk=1+k+k2+k3+…+klm^k = 1 + k + k^2 + k^3 + \ldots + k^l.
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