It seems easy
For each positive integer \color{}{k} , let \color{}{S_k} denote the increasing arithmetic sequence of integers whose first term is \color{}{1} and whose common difference is \color{} {k} . For how many values of \color{} {k} does \color{}{S_k} contain the term \color{} {2005} .
The answer is 12.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
we need to find all the factors of 2005-1 ie 2004, which are- 1, 2004 2, 1002 3, 668 4, 501 6, 334 12, 167
So 12 values of k