MathDB
Polynomial with integer coefficients

Source: AMC 12B 2010, Problem 21

February 25, 2010
algebrapolynomialnumber theoryleast common multiplefloor functionbinomial theoremAMC

Problem Statement

Let a>0 a>0, and let P(x) P(x) be a polynomial with integer coefficients such that P(1)\equal{}P(3)\equal{}P(5)\equal{}P(7)\equal{}a\text{, and} P(2)\equal{}P(4)\equal{}P(6)\equal{}P(8)\equal{}\minus{}a\text{.} What is the smallest possible value of a a? <spanclass=′latex−bold′>(A)</span> 105<spanclass=′latex−bold′>(B)</span> 315<spanclass=′latex−bold′>(C)</span> 945<spanclass=′latex−bold′>(D)</span> 7!<spanclass=′latex−bold′>(E)</span> 8! <span class='latex-bold'>(A)</span>\ 105 \qquad <span class='latex-bold'>(B)</span>\ 315 \qquad <span class='latex-bold'>(C)</span>\ 945 \qquad <span class='latex-bold'>(D)</span>\ 7! \qquad <span class='latex-bold'>(E)</span>\ 8!
Back to ProblemsView on AoPS