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Number Theory Level 5

Find the number of ordered pairs of positive integers ( x , y ) (x,y) such that the following equation is satisfied,

x + y 2 + z 3 = x y z x+y^{2}+z^{3}=xyz

where z = gcd ⁡ ( x , y ) z=\gcd(x,y) .


The answer is 4.

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Siddharth Singh by Siddharth Singh , 20, India

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1 solution

Kazem Sepehrinia
Dec 31, 2015

This is one of the best Olympiad Diophantine equations ever :-) I have posted it before: To bound or not to bound

2 Helpful 0 Interesting 0 Brilliant 1 Confused

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