My Math Forum Proof involving a field and prime numbers

 Abstract Algebra Abstract Algebra Math Forum

 January 19th, 2012, 02:51 PM #1 Newbie   Joined: Jan 2012 Posts: 2 Thanks: 0 Proof involving a field and prime numbers Hi, I'm in Linear Algebra II and we're currently studying vector spaces over fields and rings. I was asked to do the following proof: Prove that if F is a field then either the result of repeatedly adding 1 to itself is always different from 0, or else the first time that it is equal to zero is when the number of summands is a prime number. I have no idea where to start with this. We did a few proofs in class showing how Zn is a field only when n is prime, which makes me believe this proof has something to do with modulus, but I'm not sure where to begin. How can I prove this?
 January 28th, 2012, 02:03 AM #2 Member   Joined: Jul 2011 From: Trieste but ever Naples in my heart! Italy, UE. Posts: 62 Thanks: 0 You use the characteristic of a ring; an hint: let $A$ be an unitary ring, you study the function $c:n\in\mathbb{Z}\to n\cdot1\in A$!

 Tags field, involving, numbers, prime, proof

### series involving prime numbers

Click on a term to search for related topics.
 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post EvanJ Advanced Statistics 0 December 5th, 2013 05:08 PM bilano99 Algebra 2 July 25th, 2013 05:42 AM Eureka Number Theory 4 November 3rd, 2012 03:51 AM queenie_n Complex Analysis 5 October 17th, 2012 05:20 PM everk Real Analysis 2 September 5th, 2011 01:06 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top