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Let \(f(n)\) return the number of distinct ordered pairs of positive integers \((a,b)\) such that for each ordered pair, \(a^2 + b^2 = n\). Note that when \(a \neq b\)\((a, b)\), and \((b, a)\) are distinct. What is the smallest positive integer \(n\) for which \(f(n) = 3\).

 

Post with explanation please.

 Sep 2, 2021
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The smallest n that works is 200, because the only ordered pairs (a,b) such that a^2 + b^2 = 200 are (2,14), (10,10), and (14,2).

 Sep 2, 2021

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