MathDB

2018-2019 Fall OMO Problem 27

Source:

November 7, 2018

Online Math Open

Problem Statement

Let

p=2^{16}+1

be a prime. Let

x,y,z

be the number of ordered tuples

(A,B,C,D,E,F)

of integers between

0

and

p-1

, inclusive, such that there exist integers

x,y,z

not all divisible by

p

with

p

dividing all three of

Ax+Ez+Fy, By+Dz+Fx, Cz+Dy+Ex

. Compute the remainder when

N

is divided by

10^6

.
Proposed by Vincent Huang

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