MathDB

Let

f: \mathbb{Z}^2\to \mathbb{R}

be a function. It is known that for any integer

C

the four functions of

x

f(x,C), f(C,x), f(x,x+C), f(x, C-x)

are polynomials of degree at most

100

. Prove that

f

is equal to a polynomial in two variables and find its maximal possible degree.
Remark: The degree of a bivariate polynomial

P(x,y)

is defined as the maximal value of

i+j

over all monomials

x^iy^j

appearing in

P

with a non-zero coefficient.

Problem Statement