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Turkey NMO 2007 1st Round - P22 (Number Theory)

Source:

October 5, 2012
modular arithmetic

Problem Statement

Let nn and mm be integers such that n≤2007≤mn\leq 2007 \leq m and nn≡−1≡mm(mod5)n^n \equiv -1 \equiv m^m \pmod 5. What is the least possible value of m−nm-n?
<spanclass=′latex−bold′>(A)</span> 4<spanclass=′latex−bold′>(B)</span> 5<spanclass=′latex−bold′>(C)</span> 6<spanclass=′latex−bold′>(D)</span> 7<spanclass=′latex−bold′>(E)</span> 8 <span class='latex-bold'>(A)</span>\ 4 \qquad<span class='latex-bold'>(B)</span>\ 5 \qquad<span class='latex-bold'>(C)</span>\ 6 \qquad<span class='latex-bold'>(D)</span>\ 7 \qquad<span class='latex-bold'>(E)</span>\ 8
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