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2010 smo (4)

Source: 2010 China South East Mathematical Olympiad

July 18, 2011
number theory unsolvednumber theory

Problem Statement

Let aa and bb be positive integers such that 1≤a<b≤1001\leq a<b\leq 100. If there exists a positive integer kk such that ab∣ak+bkab|a^k+b^k, we say that the pair (a,b)(a, b) is good. Determine the number of good pairs.
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