Talk:Advanced modular arithmetic theory

Intro

This article in its current form is dog crap, and needs to be re-written. It is meant to be provide an advanced expostion of modular arithmetic that goes beyond the scope of the more basic article modular arithmetic.

Agreed--this has almost nothing "advanced" in it. Most of this ought to be/is in the basic article. I would vote that instead of having this article, we link to more advanced articles from the basic article.

Theorems about primality tests
Structure of the multiplicative group of integers modulo n
Lagrange's theorem about polynomials mod primes (at most deg(p) roots)
Quadratic residue
Quadratic reciprocity
Primitive roots

--Superninja 06:39, 10 Mar 2005 (UTC)

Most of this stuff is in the basic article. The stuff which is not, is on purpose. I, and other people, think that the extra stuff in here does not fit well with what is already in modular arithmetic (it is poorly written, and jumps a bit in the level of knowledge required).

But all of this is debatable. I would be very happy to discuss this with you.

I agree with you that this article is worthless. If it stays longer that way, I could even submit it for deletion or redirect it.

If you have time, could you please improve on this article? (I don't have the necessary background). Linas who contributed the material in here (second half) seems to not care much about it, except for doing the cut & paste thing (if you check the history). Oleg Alexandrov 16:05, 10 Mar 2005 (UTC)

Question

Linas wrote in the article:

The first encyclopedia entry on modular arithmetic was written by Euclid, in Book 7 of Euclid's Elements.

Now, was it encyclopedia what Euclid wrote? The Euclid's Elements page says it was a mathematical treatise, aka, an Abramowitz and Stegun before its time. Oleg Alexandrov 22:11, 5 Feb 2005 (UTC)

Yes well, encyclopedia is an 18th century Enlightnment concept, so, by definition, anything written before that time cannot technically be called an encyclopedia. On the other hand, the Elements, along with Aristotle's works and Pliny's History, come close to what in modern times would be called an "encyclopedia". So I think the usage is entirely approriate. A&S is an excellent reference work, but its neither encylopeadic nor is it a treatise. linas 00:17, 6 Feb 2005 (UTC)

Now we are getting into fine points about what an encyclopedia is, and whether Euclid wrote about modular arithmetic or ordinary arithmetic. Thus, never mind. Could you check the talk page of Fixed point theorems in infinite-dimensional spaces? I have a question there about the paragaph you inserted. Thanks. Oleg Alexandrov 02:16, 6 Feb 2005 (UTC)