2005 AIME I Problems/Problem 2
For each positive integer let denote the increasing arithmetic sequence of integers whose first term is 1 and whose common difference is For example, is the sequence For how many values of does contain the term 2005?
Suppose that the nth term of the sequence is 2005. Then so The ordered pairs of positive integers that satisfy the last equation are ,, , , , , ,, , , , and . Thus the requested number of values is 12.