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a+b+c=a^2+b^2+c^2 \in Z, abc = m^2/n^3 (HOMC 2016 S Q9)

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September 8, 2019
number theoryalgebrarelatively primeRational Root Theorem

Problem Statement

Let rational numbers a,b,ca, b, c satisfy the conditions a+b+c=a2+b2+c2∈Za + b + c = a^2 + b^2 + c^2 \in Z. Prove that there exist two relative prime numbers m,nm, n such that abc=m2n3abc =\frac{m^2}{n^3} .
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