MathDB

3

Part of 1994 Irish Math Olympiad

Problems(2)

polynomials

Source: Ireland 1994

6/29/2009
Find all real polynomials f(x) f(x) satisfying f(x^2)\equal{}f(x)f(x\minus{}1) for all x x.
algebrapolynomialinductionalgebra unsolved
inequality

Source: Ireland 1994

6/29/2009
Prove that for every integer n>1 n>1, n((n\plus{}1)^{\frac{2}{n}}\minus{}1)<\displaystyle\sum_{i\equal{}1}^{n}\frac{2i\plus{}1}{i^2}
inequalitiesinequalities proposed