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2017 Algebra/NT #8: (a+b)(a+b+1)/ab is an integer

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February 19, 2017

Problem Statement

Consider all ordered pairs of integers (a,b)(a,b) such that 1≤a≤b≤1001\le a\le b\le 100 and (a+b)(a+b+1)ab\frac{(a+b)(a+b+1)}{ab} is an integer.
Among these pairs, find the one with largest value of bb. If multiple pairs have this maximal value of bb, choose the one with largest aa. For example choose (3,85)(3,85) over (2,85)(2,85) over (4,84)(4,84). Note that your answer should be an ordered pair.
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