MathDB

A sequence of integers fsng is defined as follows: fix integers

a

b

c

, and

d

, then set

s_1 = a

s_2 = b

, and

s_n = cs_{n-1} + ds_{n-2}

for all

n \ge 3

. Create a second sequence

\{t_n\}

by defining each

t_n

to be the remainder when

s_n

is divided by

2018

(so we always have

0 \le t_n \le 2017

). Let

N = (2018^2)!

. Prove that

t_N = t_{2N}

regardless of the choices of

a

b

c

, and

d

Problem Statement