Waste less time on Facebook — follow Brilliant.
×

Generalizing Zsigmondy's Theorem

Main post link -> http://en.wikipedia.org/wiki/Zsigmondy's_theorem

I know that there are some generalizations of this extremely neat and beautiful result over some extensions of \(\mathbb{Z}\), more precisely I'm speaking of Gaussian Integers (proving it over any other quadratic extension would also be of great help). It would be nice if someone could point out some ideas, which I could follow to prove the result. For those who eager to help, but don't know where to start, try getting used with Cyclotomic Polynomials and classic proof of Zsigmondy's Theorem.

From the first glance the theorem may appear useless, but it really is an Olympiad gem, which sometimes cracks a quite hard question.

Note by Nicolae Sapoval
4 years, 6 months ago

No vote yet
1 vote

  Easy Math Editor

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 \( 2 \times 3 \)
2^{34} \( 2^{34} \)
a_{i-1} \( a_{i-1} \)
\frac{2}{3} \( \frac{2}{3} \)
\sqrt{2} \( \sqrt{2} \)
\sum_{i=1}^3 \( \sum_{i=1}^3 \)
\sin \theta \( \sin \theta \)
\boxed{123} \( \boxed{123} \)

Comments

There are no comments in this discussion.

×

Problem Loading...

Note Loading...

Set Loading...