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Set of Integers

Source: 1964 AHSME #16

October 21, 2012
AMC

Problem Statement

Let f(x)=x2+3x+2f(x)=x^2+3x+2 and let SS be the set of integers {0,1,2,…,25}\{0, 1, 2, \dots , 25 \}. The number of members ss of SS such that f(s)f(s) has remainder zero when divided by 6 is:
<spanclass=′latex−bold′>(A)</span> 25<spanclass=′latex−bold′>(B)</span> 22<spanclass=′latex−bold′>(C)</span> 21<spanclass=′latex−bold′>(D)</span> 18<spanclass=′latex−bold′>(E)</span> 17{{ <span class='latex-bold'>(A)</span>\ 25\qquad<span class='latex-bold'>(B)</span>\ 22\qquad<span class='latex-bold'>(C)</span>\ 21\qquad<span class='latex-bold'>(D)</span>\ 18 }\qquad<span class='latex-bold'>(E)</span>\ 17 }
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