
Abstract Algebra Abstract Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
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 be an unitary ring, you study the function !


Tags 
field, involving, numbers, prime, proof 
Search tags for this page 
Click on a term to search for related topics.

Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Probability Questions Involving 64 Numbers  EvanJ  Advanced Statistics  0  December 5th, 2013 05:08 PM 
Equation Involving Complex Numbers  bilano99  Algebra  2  July 25th, 2013 05:42 AM 
The paradox between prime numbers and natural numbers.  Eureka  Number Theory  4  November 3rd, 2012 03:51 AM 
Simultaneous equations involving complex numbers?! STRESSS!!  queenie_n  Complex Analysis  5  October 17th, 2012 05:20 PM 
Series Involving Prime Numbers  everk  Real Analysis  2  September 5th, 2011 01:06 PM 