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January 19th, 2012, 03:51 PM   #1
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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?
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January 28th, 2012, 03:03 AM   #2
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You use the characteristic of a ring; an hint: let be an unitary ring, you study the function !
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