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Number of natural solutions (a,b)

Source: Swiss Math Olympiad 2010 - final round, problem 3

March 16, 2010
number theory proposednumber theory

Problem Statement

For nāˆˆN n\in\mathbb{N}, determine the number of natural solutions (a,b) (a,b) such that (4a\minus{}b)(4b\minus{}a)\equal{}2010^n holds.
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