MathDB

BMT 2022 Fall Discrete P8

Source:

May 6, 2023

recursionDiscrete

Problem Statement

Define the two sequences

a_0, a_1, a_2, \cdots

and

b_0, b_1, b_2, \cdots

by

a_0 = 3

and

b_0 = 1

with the recurrence relations

a_{n+1} = 3a_n + b_n

and

b_{n+1} = 3b_n - a_n

for all nonnegative integers

n.

Let

r

and

s

be the remainders when

a_{32}

and

b_{32}

are divided by

31,

respectively. Compute

100r + s.

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