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2^c + 2^{2016} = a^b with b>1, and a,b,c naturals

Source: Indonesia MO (INAMO) 2016 P2

September 14, 2018
Diophantine equationnumber theory

Problem Statement

Determine all triples of natural numbers (a,b,c)(a,b, c) with b>1b> 1 such that 2c+22016=ab2^c + 2^{2016} = a^b.
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