MathDB

1

Part of 1996 Iran MO (3rd Round)

Problems(2)

Inequality with 4 variables - \sum \frac{a}{b+2c+3d} ≥ 2/3

Source: Iran Third Round 1997, E1, P1

3/27/2011
Let a,b,c,da,b,c,d be positive real numbers. Prove that ab+2c+3d+bc+2d+3a+cd+2a+3b+da+2b+3c≥23.\frac{a}{b+2c+3d}+\frac{b}{c+2d+3a}+\frac{c}{d+2a+3b}+\frac{d}{a+2b+3c} \geq \frac{2}{3}.
inequalitiesinequalities proposed
On the equation 2^x + 3^y = z^2 (old)

Source: Iran Third Round 1996, E2, P1

3/25/2011
Find all non-negative integer solutions of the equation 2x+3y=z2.2^x + 3^y = z^2 .
number theory proposednumber theory