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Turkish NMO First Round - 2012 Problem - 02 {Number Theory}

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July 1, 2012

Problem Statement

Find the sum of distinct residues of the number 2012n+m22012^n+m^2 on mod  11\mod 11 where mm and nn are positive integers.
<spanclass=′latex−bold′>(A)</span> 55<spanclass=′latex−bold′>(B)</span> 46<spanclass=′latex−bold′>(C)</span> 43<spanclass=′latex−bold′>(D)</span> 39<spanclass=′latex−bold′>(E)</span> 37 <span class='latex-bold'>(A)</span>\ 55 \qquad <span class='latex-bold'>(B)</span>\ 46 \qquad <span class='latex-bold'>(C)</span>\ 43 \qquad <span class='latex-bold'>(D)</span>\ 39 \qquad <span class='latex-bold'>(E)</span>\ 37
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