I'm currently in Linear Algebra II and I'm unsure how to proceed with the following proof:
Prove that if F is a field then either the result of repeatedly adding 1 to itself is always different than from 0, or else the first time that it is equal to zero occurs when the number of summands is a prime number.
We've done proofs on why Zn is a field only when n is prime, which makes me think the question is linked to modulus in some way. I'm simply just not sure how to start this proof - how can I prove adding 1 to a number is different from adding 0? Shouldn't that be defined in the set of numbers we're working with?
Thanks for any help!