MathDB

3

Part of 2010 Germany Team Selection Test

Problems(2)

3^m-7^n=2

Source: VAIMO 3, German Pre-TST 2010

7/16/2011
Determine all (m,n)∈Z+×Z+(m,n) \in \mathbb{Z}^+ \times \mathbb{Z}^+ which satisfy 3m−7n=2.3^m-7^n=2.
inductionDiophantine equationnumber theory unsolvednumber theory
f(x)f(y) = (x+y+1)^2 * f((xy-1)/(x+y+1))

Source: AIMO 5/3, German TST 2010

7/16/2011
Find all functions f:R→Rf: \mathbb{R} \to \mathbb{R} such that f(x)f(y)=(x+y+1)2⋅f(xy−1x+y+1)f(x)f(y) = (x+y+1)^2 \cdot f \left( \frac{xy-1}{x+y+1} \right) ∀x,y∈R\forall x,y \in \mathbb{R} with x+y+1≠0x+y+1 \neq 0 and f(x)>1f(x) > 1 ∀x>0.\forall x > 0.
functiontrigonometryalgebrafunctional equationalgebra unsolved