3

Part of 2010 Switzerland - Final Round

Problems(1)

Number of natural solutions (a,b)

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

n\in\mathbb{N}

, determine the number of natural solutions

(a,b)

such that (4a\minus{}b)(4b\minus{}a)\equal{}2010^n holds.

number theory proposednumber theory