(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let M_n= 2^(n) - 1 be the n-th Mersenne number.

a) Show that, if m|n, then M_m|M_n

b) Show that, if m<n and m does not divide n, then GCD(M_n,M_m) = GCD(M_m,M_r) where r is the remainder of n upon division by m

c) Let m,n be arbitrary natural numbers, and let d = GCD(m,n). Using the above results, show that GCD(M_n,M_n) = M_d

2. The attempt at a solution

So I figured out part a quite easily, by letting n=mk and using congruences, but I'm stuck on part b as im unsure whether this can by proved using only congruences or if I need to incorporate the Euclidean algorithm. Any ideas?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Divisibility of Mersenne numbers?

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**