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n = \frac{1}{2}(a + b - 1)(a + b - 2) + a

Source: Indian National Maths Olympiad, Problem 2

February 5, 2006
algebra proposedalgebra

Problem Statement

Prove that for every positive integer nn there exists a unique ordered pair (a,b)(a,b) of positive integers such that n=12(a+b−1)(a+b−2)+a. n = \frac{1}{2}(a + b - 1)(a + b - 2) + a .
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