My Math Forum Proof involving a field and prime numbers

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 January 19th, 2012, 03:51 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, 03:03 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 $c:n\in\mathbb{Z}\to n\cdot1\in A$!

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