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Found problems: 2

2011 Hanoi Open Mathematics Competitions, 9
For every pair of positive integers $(x, y)$ we de fine $f(x,y)$ as follows: $f(x,1) = x$ $f(x,y) = 0$ if $y > x$ $f(x +1,y) = y[f(x,y)+ f(x, y-1)]$ Evaluate $f(5, 5)$.
function positive integer two variables functional equations number theory

2019 Tournament Of Towns, 1
The polynomial P(x,y) is such that for every integer n >= 0 each of the polynomials P(x,n) and P(n,y) either is a constant zero or has a degree not greater than n. Is it possible that P(x,x) has an odd degree?
polynomial two variables algebra polynomials