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a^n + 2^n divides b^n + c

Source: North Korea Team Selection Test 2013 #3

May 17, 2014
modular arithmeticquadraticsnumber theoryNorth KoreaTSTDivisibility

Problem Statement

Find all a,b,c∈Z a, b, c \in \mathbb{Z} , c≥0 c \ge 0 such that an+2n∣bn+c a^n + 2^n | b^n + c for all positive integers n n where 2ab 2ab is non-square.
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