1989 USAMO Problems/Problem 1
Problem
For each positive integer , let
.
Find, with proof, integers such that
and
.
Solution
If we re-group the terms of ,
Thus, for ,
.
For the second part, applying this result gives
For , we get that
.
See also
1989 USAMO (Problems • Resources) | ||
Preceded by First question |
Followed by Problem 2 | |
1 • 2 • 3 • 4 • 5 | ||
All USAMO Problems and Solutions |