MathDB

1

Part of 2010 Korea National Olympiad

Problems(2)

21 distinct prime divisors

Source: Korea National Olympiad 2010 Problem 1

9/9/2012
Prove that 7220+7219+1 7^{2^{20}} + 7^{2^{19}} + 1 has at least 21 21 distinct prime divisors.
modular arithmeticlogarithmsnumber theory proposednumber theory
An inequality with x+y+z=1

Source: Korea National Olympiad 2010 Problem 5

9/9/2012
x,y,z x, y, z are positive real numbers such that x+y+z=1 x+y+z=1 . Prove that x1−x+y1−y+z1−z>2 \sqrt{ \frac{x}{1-x} } + \sqrt{ \frac{y}{1-y} } + \sqrt{ \frac{z}{1-z} } > 2
inequalitiestrigonometryAMCUSA(J)MOUSAMOinequalities proposed