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P34 [Number Theory] - Turkish NMO 1st Round - 2005

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October 26, 2013

Problem Statement

How many triples (x,y,z)(x,y,z) of positive integers are there such that xyz=510510xyz=510510 and x2y+y2z+z2x=xy2+yz2+zx2x^2y+y^2z+z^2x = xy^2 + yz^2 + zx^2?
<spanclass=′latex−bold′>(A)</span> 0<spanclass=′latex−bold′>(B)</span> 1<spanclass=′latex−bold′>(C)</span> 3<spanclass=′latex−bold′>(D)</span> 8<spanclass=′latex−bold′>(E)</span> None of above <span class='latex-bold'>(A)</span>\ 0 \qquad<span class='latex-bold'>(B)</span>\ 1 \qquad<span class='latex-bold'>(C)</span>\ 3 \qquad<span class='latex-bold'>(D)</span>\ 8 \qquad<span class='latex-bold'>(E)</span>\ \text{None of above}
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