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P18 [Number Theory] - Turkish NMO 1st Round - 2003

Source:

May 16, 2014
modular arithmetic

Problem Statement

What is the least integer n>2003n>2003 such that 5n+n55^n + n^5 is a multiple of 1111?
<spanclass=′latex−bold′>(A)</span> 2010<spanclass=′latex−bold′>(B)</span> 2011<spanclass=′latex−bold′>(C)</span> 2012<spanclass=′latex−bold′>(D)</span> 2014<spanclass=′latex−bold′>(E)</span> None of the preceding <span class='latex-bold'>(A)</span>\ 2010 \qquad<span class='latex-bold'>(B)</span>\ 2011 \qquad<span class='latex-bold'>(C)</span>\ 2012 \qquad<span class='latex-bold'>(D)</span>\ 2014 \qquad<span class='latex-bold'>(E)</span>\ \text{None of the preceding}
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