MathDB

3

Part of 1989 IberoAmerican

Problems(2)

Side lengths of a triangle inequality

Source: IberoAmerican 1989 Q3

11/27/2010
Let a,ba,b and cc be the side lengths of a triangle. Prove that: a−ba+b+b−cb+c+c−ac+a<116\frac{a-b}{a+b}+\frac{b-c}{b+c}+\frac{c-a}{c+a}<\frac{1}{16}
inequalitiesinequalities proposed
Infinitely many solutions to diophantine equation

Source: IberoAmerican 1989 Q6

11/27/2010
Show that the equation 2x2−3x=3y22x^2-3x=3y^2 has infinitely many solutions in positive integers.
modular arithmeticDiophantine equationnumber theory proposednumber theory