1988 AIME Problems/Problem 8
Problem
The function , defined on the set of ordered pairs of positive integers, satisfies the following properties:
Calculate
.
Solution
Since all of the function's properties contain a recursive definition except for the first one, we know that in order to obtain an integer answer. So, we have to transform
to this form by exploiting the other properties. The second one doesn't help us immediately, so we will use the third one.
Note that
Repeating the process several times,
See also
1988 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 7 |
Followed by Problem 9 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |