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Units Digit of a Binomial Expansion

Source:

January 18, 2009
modular arithmetic

Problem Statement

Find the units digit of the decimal expansion of (15 \plus{} \sqrt{220})^{19} \plus{} (15 \plus{} \sqrt{220})^{82}. <spanclass=′latex−bold′>(A)</span> 0<spanclass=′latex−bold′>(B)</span> 2<spanclass=′latex−bold′>(C)</span> 5<spanclass=′latex−bold′>(D)</span> 9<spanclass=′latex−bold′>(E)</span> none of these <span class='latex-bold'>(A)</span>\ 0\qquad <span class='latex-bold'>(B)</span>\ 2\qquad <span class='latex-bold'>(C)</span>\ 5\qquad <span class='latex-bold'>(D)</span>\ 9\qquad <span class='latex-bold'>(E)</span>\ \text{none of these}
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