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Two Arithmetic Progressions

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January 15, 2009
modular arithmetic

Problem Statement

Let 1,4,⋯ 1,4,\cdots and 9,16,⋯ 9,16,\cdots be two arithmetic progressions. The set S S is the union of the fi rst 2004 2004 terms of each sequence. How many distinct numbers are in S S? <spanclass=′latex−bold′>(A)</span> 3722<spanclass=′latex−bold′>(B)</span> 3732<spanclass=′latex−bold′>(C)</span> 3914<spanclass=′latex−bold′>(D)</span> 3924<spanclass=′latex−bold′>(E)</span> 4007 <span class='latex-bold'>(A)</span>\ 3722\qquad <span class='latex-bold'>(B)</span>\ 3732\qquad <span class='latex-bold'>(C)</span>\ 3914\qquad <span class='latex-bold'>(D)</span>\ 3924\qquad <span class='latex-bold'>(E)</span>\ 4007
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