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Introduction to Number Theory  Homework on 8

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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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