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Fermat's Little Theorem

Source: 2017 AMC 10B #14

February 16, 2017
AMCAMC 10AMC 10 Bnumber theory2017 AMC 10B

Problem Statement

An integer NN is selected at random in the range 1≤N≤2020.1\le N \le 2020. What is the probability that the remainder when N16N^{16} is divided by 55 is 11?
<spanclass=′latex−bold′>(A)</span> 15<spanclass=′latex−bold′>(B)</span> 25<spanclass=′latex−bold′>(C)</span> 35<spanclass=′latex−bold′>(D)</span> 45<spanclass=′latex−bold′>(E)</span> 1<span class='latex-bold'>(A)</span> \text{ }\frac{1}{5} \qquad <span class='latex-bold'>(B)</span> \text{ }\frac{2}{5} \qquad <span class='latex-bold'>(C)</span> \text{ }\frac{3}{5} \qquad <span class='latex-bold'>(D)</span> \text{ }\frac{4}{5} \qquad <span class='latex-bold'>(E)</span> \text{ 1}
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