2005 AIME II Problems/Problem 11
Let be a positive integer, and let be a sequence of integers such that and for Find
Note: Clearly, the stipulation that the sequence is composed of positive integers is a minor oversight, as the term , for example, is obviouly not integral.
For , we have
Thus the product is a monovariant: it decreases by 3 each time increases by 1. Since for we have , so when , will be zero for the first time, which implies that , our answer.