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P24 [Algebra] - Turkish NMO 1st Round - 2002

Source:

August 10, 2014
floor functiongeometry3D geometry

Problem Statement

How many positive integers nn are there such that the equation ⌊7n+23⌋=⌊7n+33⌋\left \lfloor \sqrt[3] {7n + 2} \right \rfloor = \left \lfloor \sqrt[3] {7n + 3} \right \rfloor does not hold?
<spanclass=′latex−bold′>a)</span> 0<spanclass=′latex−bold′>b)</span> 1<spanclass=′latex−bold′>c)</span> 7<spanclass=′latex−bold′>d)</span> Infinitely many<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>\ 7 \qquad<span class='latex-bold'>d)</span>\ \text{Infinitely many} \qquad<span class='latex-bold'>e)</span>\ \text{None of above}
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