Summary: Putnam Seminar 2004
More problems from "Mathematical Miniatures". Here are three shorter problems:
1. The real numbers x1, x2, . . . xn satisfy the conditions
x1 + x2 + · · · + xn = 0, x2
1 + x2
2 + · · · + x2
n = 1.
Prove that the product of some pair of these numbers is less than or equal to -1/n.
2. The positive integers x1, x2, . . . , x100 satisfy the equation
1

x1
+
1

x2
+ · · · +
1

x100

Source: Albert, John - Department of Mathematics, University of Oklahoma

Collections: Mathematics