MathDB

Number theory sequence.

Source: Poland

January 10, 2005

inductionmodular arithmeticalgebrapolynomialnumber theory proposednumber theory

Problem Statement

Let

p

be a prime number, and define a sequence by:

x_i=i

for

i=,0,1,2...,p-1

and

x_n=x_{n-1}+x_{n-p}

for

n \geq p

Find the remainder when

x_{p^3}

is divided by

p