2002 USA TST Problems
Problems from the 2002 USA TST.
Let be a triangle. Prove that
Let be a prime number greater than 5. For any integer , define
Prove that for all positive integers and the numerator of , when written in lowest terms, is divisible by .
Let be an integer greater than 2, and distinct points in the plane. Let denote the union of all segments . Determine if it is always possible to find points and in such that (segment can lie on line ) and , where (1) ; (2) .