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Hundreds digits of 2011^{2011}

Source: AMC 10 2011 b Problem 23

February 25, 2011
modular arithmeticEulerfunctionnumber theoryleast common multiplesearchLaTeX

Problem Statement

What is the hundreds digit of 201120112011^{2011}?
<spanclass=′latex−bold′>(A)</span> 1<spanclass=′latex−bold′>(B)</span> 4<spanclass=′latex−bold′>(C)</span> 5<spanclass=′latex−bold′>(D)</span> 6<spanclass=′latex−bold′>(E)</span> 9 <span class='latex-bold'>(A)</span>\ 1 \qquad <span class='latex-bold'>(B)</span>\ 4 \qquad <span class='latex-bold'>(C)</span>\ 5 \qquad <span class='latex-bold'>(D)</span>\ 6 \qquad <span class='latex-bold'>(E)</span>\ 9
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