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P31 [Number Theory] - Turkish NMO 1st Round - 2001

Source:

April 23, 2014

Problem Statement

What is the largest integer nn such that 2n+652^n + 65 is equal to square of an integer?
<spanclass=′latex−bold′>(A)</span> 1024<spanclass=′latex−bold′>(B)</span> 268<spanclass=′latex−bold′>(C)</span> 10<spanclass=′latex−bold′>(D)</span> 4<spanclass=′latex−bold′>(E)</span> None of the preceding <span class='latex-bold'>(A)</span>\ 1024 \qquad<span class='latex-bold'>(B)</span>\ 268 \qquad<span class='latex-bold'>(C)</span>\ 10 \qquad<span class='latex-bold'>(D)</span>\ 4 \qquad<span class='latex-bold'>(E)</span>\ \text{None of the preceding}
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