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An application of Gauss-Legendre

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December 19, 2019
abstract algebramodular arithmeticnumber theoryPythagorean Triple

Problem Statement

Consider a natural number n≡9(mod25). n\equiv 9\pmod {25}. Prove that there exist three nonnegative integers a,b,c a,b,c having the property that: n=a(a+1)2+b(b+1)2+c(c+1)2 n=\frac{a(a+1)}{2} +\frac{b(b+1)}{2} +\frac{c(c+1)}{2}
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