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Putnam Seminar 2004 More problems from "Mathematical Miniatures". Here are three shorter problems
 

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