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Turkish NMO First Round - 2012 Problem - 06 {Number Theory}

Source:

July 1, 2012
modular arithmetic

Problem Statement

Which one statisfies n29≡7(mod65)n^{29} \equiv 7 \pmod {65}?
<spanclass=′latex−bold′>(A)</span> 37<spanclass=′latex−bold′>(B)</span> 39<spanclass=′latex−bold′>(C)</span> 43<spanclass=′latex−bold′>(D)</span> 46<spanclass=′latex−bold′>(E)</span> 55 <span class='latex-bold'>(A)</span>\ 37 \qquad <span class='latex-bold'>(B)</span>\ 39 \qquad <span class='latex-bold'>(C)</span>\ 43 \qquad <span class='latex-bold'>(D)</span>\ 46 \qquad <span class='latex-bold'>(E)</span>\ 55
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