2005 AIME I Problems/Problem 2
Problem
For each positive integer , let denote the increasing arithmetic sequence of integers whose first term is and whose common difference is . For example, is the sequence For how many values of does contain the term ?
Solution
Suppose that the th term of the sequence is . Then so . The ordered pairs of positive integers that satisfy the last equation are ,, , , , , ,, , , and , and each of these gives a possible value of . Thus the requested number of values is , and the answer is .
Alternatively, notice that the formula for the number of divisors states that there are divisors of .
See also
2005 AIME I (Problems • Answer Key • Resources) | ||
Preceded by Problem 1 |
Followed by Problem 3 | |
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