MA410 Homework 2
Due at 4:59pm in my mailbox in SAS 3151, Thursday, February 28, 2019
All solutions must be submitted stapled in hardcopy
either to me in class or placed in my mailbox.
Note my office hours on my
schedule.

A Mersenne number is an integer of the form M_{p} = 2^{p}  1,
where p is a prime number.
Please prove that no Mersenne prime number is a divisor of a Mersenne number
that is larger than the Mersenne prime.

Let the Fermat numbers be F_{n}= 2^{2n} + 1
for integers n ≥ 0. Please prove that 2^{Fn1}
≡ 1 (mod F_{n}) for all n ≥ 0.

ENT, §4.2, Problem 18, page 68.

ENT, §4.4, Problem 7(a), page 83,
using the Chinese remainder algorithm from class,
which is based on interpolation by divided differences.

ENT, §5.2, Problem 21, page 93.

ENT, §5.2, Problem 19, page 93.