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Infinitely many pairs exist satisfying property

Source:

July 22, 2012
number theorygreatest common divisornumber theory proposed

Problem Statement

Show that there exist infinitely many pairs (a,b)(a, b) of positive integers with the property that a+ba+b divides ab+1ab+1, a−ba-b divides ab−1ab-1, b>1b>1 and a>b3−1a>b\sqrt{3}-1
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