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Turkey NMO 2007 1st Round - P02 (Number Theory)

Source:

October 4, 2012
modular arithmetic

Problem Statement

What is the last three digits of base-4 representation of 10⋅3195⋅494910\cdot 3^{195}\cdot 49^{49}?
<spanclass=′latex−bold′>(A)</span> 112<spanclass=′latex−bold′>(B)</span> 130<spanclass=′latex−bold′>(C)</span> 132<spanclass=′latex−bold′>(D)</span> 212<spanclass=′latex−bold′>(E)</span> 232 <span class='latex-bold'>(A)</span>\ 112 \qquad<span class='latex-bold'>(B)</span>\ 130 \qquad<span class='latex-bold'>(C)</span>\ 132 \qquad<span class='latex-bold'>(D)</span>\ 212 \qquad<span class='latex-bold'>(E)</span>\ 232
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