10

Part of 1993 Poland - First Round

Problems(1)

On values of (1-p^m)^n+(1-q^n)^m

Source: Poland Math Olympiad 1993 Round 1 #10

Given positive real numbers

p,q

p+q=1

. Prove that for all positive integers

m,n

the following inequality holds

(1-p^m)^n+(1-q^n)^m \geq 1