MathDB
P34 [Number Theory] - Turkish NMO 1st Round - 2002

Source:

August 11, 2014
geometry3D geometrymodular arithmetic

Problem Statement

How many positive integers nn are there such that 3n2+3n+73n^2 + 3n + 7 is a perfect cube?
<spanclass=latexbold>a)</span> 0<spanclass=latexbold>b)</span> 1<spanclass=latexbold>c)</span> 3<spanclass=latexbold>d)</span> 7<spanclass=latexbold>e)</span> Infinitely many <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>\ 7 \qquad<span class='latex-bold'>e)</span>\ \text{Infinitely many}