2005 AIME II Problems/Problem 11
Problem
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 integers is a minor oversight, as the term , for example, is obviouly not integral.
Solution
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.