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Turkey NMO 2008 1st Round - P02 (Number Theory)

Source:

August 24, 2012
modular arithmeticquadraticsAMCUSA(J)MOUSAMO

Problem Statement

For which value of AA, does the equation 3m2n=n3+A3m^2n = n^3 + A have a solution in natural numbers?
<spanclass=′latex−bold′>(A)</span> 301<spanclass=′latex−bold′>(B)</span> 403<spanclass=′latex−bold′>(C)</span> 415<spanclass=′latex−bold′>(D)</span> 427<spanclass=′latex−bold′>(E)</span> 481 <span class='latex-bold'>(A)</span>\ 301 \qquad<span class='latex-bold'>(B)</span>\ 403 \qquad<span class='latex-bold'>(C)</span>\ 415 \qquad<span class='latex-bold'>(D)</span>\ 427 \qquad<span class='latex-bold'>(E)</span>\ 481
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