MathDB
Two-variable function

Source: VAIMO 4, German Pre-TST 2002

July 17, 2011
functionquadraticsIMO Shortlistalgebra unsolvedalgebra

Problem Statement

Let PP denote the set of all ordered pairs (p,q) \left(p,q\right) of nonnegative integers. Find all functions f:Pā†’Rf: P \rightarrow \mathbb{R} satisfying f(p,q) \equal{} \begin{cases} 0 & \text{if} \; pq \equal{} 0, \\ 1 \plus{} \frac{1}{2} f(p+1,q-1) \plus{} \frac{1}{2} f(p-1,q+1) & \text{otherwise} \end{cases}
Compare IMO shortlist problem 2001, algebra A1 for the three-variable case.
Back to ProblemsView on AoPS