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P10 [Number Theory] - Turkish NMO 1st Round - 2002

Source:

August 8, 2014
modular arithmeticgeometry3D geometry

Problem Statement

Which of the following does not divide the number of ordered pairs (x,y)(x,y) of integers satisfying the equation x3−13y3=1453x^3 - 13y^3 = 1453?
<spanclass=′latex−bold′>a)</span> 2<spanclass=′latex−bold′>b)</span> 3<spanclass=′latex−bold′>c)</span> 5<spanclass=′latex−bold′>d)</span> 7<spanclass=′latex−bold′>e)</span> None of above <span class='latex-bold'>a)</span>\ 2 \qquad<span class='latex-bold'>b)</span>\ 3 \qquad<span class='latex-bold'>c)</span>\ 5 \qquad<span class='latex-bold'>d)</span>\ 7 \qquad<span class='latex-bold'>e)</span>\ \text{None of above}
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