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1990 AMC 12 #30

Source:

December 31, 2011
algebrapolynomialAMC

Problem Statement

If Rn=12(an+bn)R_n=\frac{1}{2}(a^n+b^n) where a=3+22a=3+2\sqrt{2}, b=3−22b=3-2\sqrt{2}, and n=0,1,2,...,n=0,1,2, ..., then R12345R_{12345} is an integer. Its units digit is
<spanclass=′latex−bold′>(A)</span> 1<spanclass=′latex−bold′>(B)</span> 3<spanclass=′latex−bold′>(C)</span> 5<spanclass=′latex−bold′>(D)</span> 7<spanclass=′latex−bold′>(E)</span> 9 <span class='latex-bold'>(A)</span>\ 1 \qquad<span class='latex-bold'>(B)</span>\ 3 \qquad<span class='latex-bold'>(C)</span>\ 5 \qquad<span class='latex-bold'>(D)</span>\ 7 \qquad<span class='latex-bold'>(E)</span>\ 9
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