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Turkey NMO 2000 1st Round - P26 (Number Theory)

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July 25, 2012

Problem Statement

Let f(x)=x3+7x2+9x+10f(x)=x^3+7x^2+9x+10. Which value of pp satisfies the statement f(a)≡f(b) (mod p)⇒a≡b (mod p) f(a) \equiv f(b) \ (\text{mod } p) \Rightarrow a \equiv b \ (\text{mod } p) for every integer a,ba,b?
<spanclass=′latex−bold′>(A)</span> 5<spanclass=′latex−bold′>(B)</span> 7<spanclass=′latex−bold′>(C)</span> 11<spanclass=′latex−bold′>(D)</span> 13<spanclass=′latex−bold′>(E)</span> 17 <span class='latex-bold'>(A)</span>\ 5 \qquad<span class='latex-bold'>(B)</span>\ 7 \qquad<span class='latex-bold'>(C)</span>\ 11 \qquad<span class='latex-bold'>(D)</span>\ 13 \qquad<span class='latex-bold'>(E)</span>\ 17
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