MathDB
2016-2017 Fall OMO Problem 24

Source:

November 16, 2016
Online Math Open

Problem Statement

Let P(x,y)P(x,y) be a polynomial such that deg⁡x(P),deg⁡y(P)≤2020\deg_x(P), \deg_y(P)\le 2020 and P(i,j)=(i+ji)P(i,j)=\binom{i+j}{i} over all 202122021^2 ordered pairs (i,j)(i,j) with 0≤i,j≤20200\leq i,j\leq 2020. Find the remainder when P(4040,4040)P(4040, 4040) is divided by 20172017.
Note: deg⁡x(P)\deg_x (P) is the highest exponent of xx in a nonzero term of P(x,y)P(x,y). deg⁡y(P)\deg_y (P) is defined similarly.
Proposed by Michael Ren
Back to ProblemsView on AoPS