MathDB

3

Part of 2012 Irish Math Olympiad

Problems(2)

Finding polynomials

Source:

4/12/2017
Find, with proof, all polynomials ff such that ff has nonnegative integer coefficients, ff(11) = 88 and ff(22) = 20122012.
PolynomialsalgebrapolynomialCombo
Inequality

Source: 2012 IrMO Paper 2 Problem 3

2/16/2018
Suppose a,b,ca,b,c are positive numbers. Prove that (ab+bc+ca+1)2≥(2a+b+c)(2a+1b+1c)\left(\frac{a}{b}+\frac{b}{c}+\frac{c}{a}+1\right)^2\ge (2a+b+c) \left(\frac{2}{a}+\frac{1}{b}+\frac{1}{c}\right) with equality if and only if a=b=ca=b=c.
inequalities