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MATH / For each positive integer k, let S_(k) denote the increasing arithmetic sequence of integers whose first term is 1 and whose common difference is k. For example, S₃ is the sequence…

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problem

For each positive integer kk, let SkS_k denote the increasing arithmetic sequence of integers whose first term is 1 and whose common difference is kk. For example, S3S_3 is the sequence 1,4,7,…1,4,7,\ldots. For how many values of kk does SkS_k contain 20052005 as a term?
Plain-text mathematical notation (without MathML)
For each positive integer k, let S_(k) denote the increasing arithmetic sequence of integers whose first term is 1 and whose common difference is k.  For example, S₃ is the sequence 1,4,7,….  For how many values of k does S_(k) contain 2005 as a term?
Original LaTeX notation
For each positive integer $k$, let $S_k$ denote the increasing arithmetic sequence of integers whose first term is 1 and whose common difference is $k$.  For example, $S_3$ is the sequence $1,4,7,\ldots$.  For how many values of $k$ does $S_k$ contain $2005$ as a term?

level

Level 5

type

Algebra

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Source and history

task_id
324c1d95-8223-528a-b798-86e25437c530
task_key
algebra--test--324c1d95-8223-528a-b798-86e25437c530
task_revision_id
1
config / split
algebra / test

Official source

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