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P27 [Number Theory] - Turkish NMO 1st Round - 2001

Source:

April 23, 2014

Problem Statement

If decimal representation of 2n2^n starts with 77, what is the first digit in decimal representation of 5n5^n?
<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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