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2017 Term Trial (Posted on 2016-02-17) Difficulty: 2 of 5
{S(D)} denotes a strictly ascending arithmetic sequence whose first term is 1 and the common difference is D, where D is a positive integer.

For how many values of D does {S(D)} contain the term 2017?

No Solution Yet Submitted by K Sengupta    
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Solution Solution Comment 1 of 1
For both 1 and 2017 to occur in an integer valued arithmetic sequence, the common difference D must be a factor of the difference 2017-1=2016.  2016 = 2^5*3^2*7^1, which means that 2016 has (5+1)*(2+1)*(1+1)  = 36 factors.  That is the answer: 36 values of D (the factors of 2016) exist such that {S(D)} contains 2017.
  Posted by Brian Smith on 2016-02-17 11:08:24
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