1992 USAMO Problems
Problem 1
Find, as a function of the sum of the digits of where each factor has twice as many digits as the previous one.
Problem 2
Prove
Problem 3
For a nonempty set of integers, let be the sum of the elements of . Suppose that is a set of positive integers with and that, for each positive integer , there is a subset of for which . What is the smallest possible value of ?
Problem 4
Chords , , and of a sphere meet at an interior point but are not contained in the same plane. The sphere through , , , and is tangent to the sphere through , , , and . Prove that .
Problem 5
Let be a polynomial with complex coefficients which is of degree and has distinct zeros.Prove that there exists complex numbers such that divides the polynomial
See Also
1992 USAMO (Problems • Resources) | ||
Preceded by 1991 USAMO |
Followed by 1993 USAMO | |
1 • 2 • 3 • 4 • 5 | ||
All USAMO Problems and Solutions |