## Description

Math 422: Introduction to Number Theory

Homework on 8

A. Silverman 8.4.

B. Let n ≥ 0.

1. Prove that

x

n+1 − 1 = (x − 1)(x

n + x

n−1 + · · · + 1).

2. Prove that

x

n+1 − y

n+1 = (x − y)

Xn

i=0

x

iy

n−i

.

C. 1. What day of the week is February 21, 2030?

2. Write a program which takes as input a year n with 2001 ≤ n ≤ 2099

and outputs the day of the week of February 21 in year n.

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