Why can't a field have exactly 6 elements? I tried to go over the axioms but couldn't figure out anything. Help please

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- Jan 24th 2008, 12:08 AMnamelessguyQuestion related to field
Why can't a field have exactly 6 elements? I tried to go over the axioms but couldn't figure out anything. Help please

- Jan 24th 2008, 12:34 AMJaneBennet
The number of elements in a finite field must be , where

*p*is a prime and*k*is a positive integer. 6 is not of the form . - Jan 24th 2008, 09:00 AMThePerfectHacker
We can make it even easier than Jane Bennet said. It can be easily proven* that the characteristic of a field (in fact an integral domain) must be or (a prime).

*)Define as .