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P10 [Number Theory] - Turkish NMO 1st Round - 2005

Source:

October 26, 2013
modular arithmeticEuler

Problem Statement

Which of the following does not divide n2225n2005n^{2225}-n^{2005} for every integer value of nn?
<spanclass=latexbold>(A)</span> 3<spanclass=latexbold>(B)</span> 5<spanclass=latexbold>(C)</span> 7<spanclass=latexbold>(D)</span> 11<spanclass=latexbold>(E)</span> 23 <span class='latex-bold'>(A)</span>\ 3 \qquad<span class='latex-bold'>(B)</span>\ 5 \qquad<span class='latex-bold'>(C)</span>\ 7 \qquad<span class='latex-bold'>(D)</span>\ 11 \qquad<span class='latex-bold'>(E)</span>\ 23