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a+b+c+d=0 and ac+bd=0, iff a-b divides 2ab

Source: Balkan MO Shortlist 2013 N8 BMO

March 10, 2020
number theorydividesIntegers

Problem Statement

Suppose that aa and bb are integers. Prove that there are integers cc and dd such that a+b+c+d=0a+b+c+d=0 and ac+bd=0ac+bd=0, if and only if aāˆ’ba-b divides 2ab2ab.
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