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P03 [Algebra] - Turkish NMO 1st Round - 2013

Source:

April 19, 2013
algebrapolynomialmodular arithmetic

Problem Statement

If the remainder is 20132013 when a polynomial with coefficients from the set {0,1,2,3,4,5}\{0,1,2,3,4,5\} is divided by x6x-6, what is the least possible value of the coefficient of xx in this polynomial?
<spanclass=latexbold>(A)</span> 5<spanclass=latexbold>(B)</span> 4<spanclass=latexbold>(C)</span> 3<spanclass=latexbold>(D)</span> 2<spanclass=latexbold>(E)</span> 1 <span class='latex-bold'>(A)</span>\ 5 \qquad<span class='latex-bold'>(B)</span>\ 4 \qquad<span class='latex-bold'>(C)</span>\ 3 \qquad<span class='latex-bold'>(D)</span>\ 2 \qquad<span class='latex-bold'>(E)</span>\ 1