Posted: Wed Oct 20, 2004 9:46 pm Post subject: How to use algebra to prove it?
I saw the following questions in Topics in Algebra. Can you use algebra to prove it?
1. If is an odd prime and if where and are integers, prove that . If , prove that .
2. Prove that , where (This should be easier)
Carto
Frequent Visitor
Joined: 29 Oct 2003Posts: 321
Location: Hong Kong
Posted: Thu Oct 21, 2004 11:12 pm Post subject:
I think the idea is that, in the field , is just a rearrangement of . These numbers sum up to be , which is a multiple of p. You can make it rigorous.
The second question should be an application of Lagrange theorem. The reduced residue system modulo is a multiplicative group of order , and is a subgroup of it.
You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot vote in polls in this forum