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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 be an unitary ring, you study the function !


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