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Turkey NMO 2007 1st Round - P10 (Number Theory)

Source:

October 4, 2012
geometry3D geometry

Problem Statement

How many positive integers n<106n<10^6 are there such that nn is equal to twice of square of an integer and is equal to three times of cube of an integer?
<spanclass=latexbold>(A)</span> 0<spanclass=latexbold>(B)</span> 1<spanclass=latexbold>(C)</span> 2<spanclass=latexbold>(D)</span> 3<spanclass=latexbold>(E)</span> None of the above <span class='latex-bold'>(A)</span>\ 0 \qquad<span class='latex-bold'>(B)</span>\ 1 \qquad<span class='latex-bold'>(C)</span>\ 2 \qquad<span class='latex-bold'>(D)</span>\ 3 \qquad<span class='latex-bold'>(E)</span>\ \text{None of the above}