MathDB

4

Part of 2005 Kazakhstan National Olympiad

Problems(2)

Functional equation

Source: Kazakhstan NMO 2005 (Final round) P4

12/16/2014
Find all functions f:Rā†’Rf :\mathbb{R}\to\mathbb{R}, satisfying the condition
f(f(x)+x+y)=2x+f(y)f(f(x)+x+y)=2x+f(y)
for any real xx and yy.
functionalgebra proposedalgebraKazakhstan
Find all polynomials

Source: From Kazakhstan NMO-2005

2/19/2008
Find all polynomials P(x) P(x) with real coefficients such that for every positive integer n n there exists a rational r r with P(r)=n P(r)=n.
algebrapolynomialalgebra proposedKazakhstan