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Divisibility relation: a^b+b | a^(2b)+2b

Source: Austrian Federal Competition 2011, part 2, #4

June 6, 2011
number theory proposednumber theory

Problem Statement

Determine all pairs (a,b)(a,b) of non-negative integers, such that ab+ba^b+b divides a2b+2ba^{2b}+2b. (Remark: 00=10^0=1.)
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