**Reference: Proofs from THE BOOK (Third Edition) (Martin Aigner and Gunter M. Ziegler)**

Suppose the set of primes, is finite and p is the largest prime. We consider the so-called *Mersenne number *, and show that any prime factor q of is bigger than p, which will yield the desired conclusion. Let q be a prime dividing , so we have .

Since p is prime, this means that the element 2 has order p in the multiplicative group of the field . This group has elements. By Lagrange’s theorem, we know that the order of every element divides the size of the group, that is, we have , and hence, .

More later,

Nalin Pithwa

### Like this:

Like Loading...

*Related*