Re: Help with theorem proof

ASM wrote:
I would appreciate if anybody could provide a clear explanation to the
theorem 12.4 on page 183 of Oliver Pretzel's book "Error Correcting
Codes and Finite Fields", OUP 1992.


Can't help you there; but if the below is the critical /step/ for
you...

I am getting stuck on the critical passage:

...'Let ord(alpha) = n and ord(beta) = m. If m does not divide n,
there must be a prime r for which the highest power x=r^k dividing m is
greater than the highest power y=r^l dividing n.' ... etc


Suppose there is a counter example m,n.

Then for every prime p where p^k divides m, p^k would also divide n. If
it didn't, then the largest power of p dividing n would be less than k,
so m,n wouldn't be a counter example..

But that would mean that m divides n, contrary to assumption.

Cheers

.

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