MathDB

2

Part of 2005 Argentina Team Selection Test

Problems(2)

Well known functional equation

Source: Argentina IMO 2005 TST, problem 2

4/28/2005
Find all functions f:R→Rf: \mathbb{R} \rightarrow \mathbb{R} such that ∀x,y∈R\forall x,y \in \mathbb{R} we have f(xf(x)+f(y))=f(x)2+yf(xf(x)+f(y)) = f(x)^2 + y
functionalgebrafunctional equationalgebra proposed
4p-3 is a perfect square

Source:

4/22/2009
Let n,pn,p be integers such that n>1n>1 and pp is a prime. If n∣p−1n\mid p-1 and p∣n3−1p\mid n^3-1, show that 4p−34p-3 is a perfect square.
number theory unsolvednumber theory