1987 USAMO Problems
Problems from the 1987 USAMO.
Find all solutions to , where m and n are non-zero integers.
The feet of the angle bisectors of form a right-angled triangle. If the right-angle is at , where is the bisector of , find all possible values for .
is the smallest set of polynomials such that:
- 1. belongs to .
- 2. If belongs to , then and both belong to .
Show that if and are distinct elements of , then for any .
M is the midpoint of XY. The points P and Q lie on a line through Y on opposite sides of Y, such that and . For what value of is a minimum?
is a sequence of 0's and 1's. T is the number of triples with which are not equal to (0, 1, 0) or (1, 0, 1). For , is the number of with plus the number of with . Show that . If n is odd, what is the smallest value of T?
|1987 USAMO (Problems • Resources)|
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The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.