MathDB

2

Part of 2012 Pan African

Problems(2)

Find all functions from reals to reals

Source: Pan African MO 2012 Day 2 Q2

10/14/2012
Find all functions f:R→R f:\mathbb{R}\rightarrow\mathbb{R} such that f(x2−y2)=(x+y)(f(x)−f(y))f(x^2 - y^2) = (x+y)(f(x) - f(y)) for all real numbers xx and yy.
functionalgebra proposedalgebra
n^m - m divides m^2 + 2m

Source: Pan African MO 2012 Day 1 Q2

10/14/2012
Find all positive integers mm and nn such that nm−mn^m - m divides m2+2mm^2 + 2m.
inequalitiesnumber theory proposednumber theory