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Arithmetic Series and Common Differences

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November 10, 2005
arithmetic sequencenumber theoryprime factorization

Problem Statement

For each positive integer kk, let SkS_k denote the increasing arithmetic sequence of integers whose first term is 11 and whose common difference is kk. For example, S3S_3 is the sequence 1,4,7,10,...1,4,7,10,.... For how many values of kk does SkS_k contain the term 20052005?
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