MathDB
P34 [Number Theory] - Turkish NMO 1st Round - 2013

Source:

April 18, 2013
geometry3D geometrymodular arithmetic

Problem Statement

How many triples of positive integers (a,b,c)(a,b,c) are there such that a!+b3=18+c3a!+b^3 = 18+c^3?
<spanclass=latexbold>(A)</span> 4<spanclass=latexbold>(B)</span> 3<spanclass=latexbold>(C)</span> 2<spanclass=latexbold>(D)</span> 1<spanclass=latexbold>(E)</span> 0 <span class='latex-bold'>(A)</span>\ 4 \qquad<span class='latex-bold'>(B)</span>\ 3 \qquad<span class='latex-bold'>(C)</span>\ 2 \qquad<span class='latex-bold'>(D)</span>\ 1 \qquad<span class='latex-bold'>(E)</span>\ 0