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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 \(f(n)=3\) ?

 

Please write an approach to get to the answer.

 Oct 21, 2021
 #1
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The only way to do this is brute force.

 

The smallest n that works is 200: 200 = 2^2 + 14^2 = 10^2 + 10^2 = 14^2 + 2^2

 Oct 21, 2021
 #2
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That is not correct, the answer is 50

 Oct 21, 2021
 #3
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Hello sherwyo,

 

how about saying Thanks to him?

I think that's not polite to each other.

 

Straight

 Oct 22, 2021

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