A useful identity

The polynomial \( x^{12} - x^7 - x^6 - x^5 + 1\) has twelve roots, all of which obviously satisfy the relation

x630−1=(x315−1)(x210−1)(x126−1)2(x90−1)(x3−1)3(x2−1)5(x−1)3(x35−1)(x15−1)2(x14−1)2(x5−1)6x68 x^{630} -1 = \frac{(x^{315}-1)(x^{210}-1)(x^{126}-1)^2 (x^{90} - 1) (x^3 - 1)^3 ( x^2 - 1)^5 (x-1)^3}{(x^{35}-1)(x^{15} - 1)^2 (x^{14} -1)^2 (x^5 - 1)^6 x^{68}}

See for yourself :)

#Algebra

Note by Levi Walker
2 years, 7 months ago

No vote yet
1 vote

  Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

  • Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
  • Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
  • Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
  • Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

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 2×3 2 \times 3
2^{34} 234 2^{34}
a_{i-1} ai−1 a_{i-1}
\frac{2}{3} 23 \frac{2}{3}
\sqrt{2} 2 \sqrt{2}
\sum_{i=1}^3 ∑i=13 \sum_{i=1}^3
\sin \theta sin⁡θ \sin \theta
\boxed{123} 123 \boxed{123}

Comments

Wow! This is so cool, but hard for me. I haven't skills in algebra, but I have skills in writing. I write a lot of cool essays and for plagiarism check I use Extra resources which really help me with many difficult writing works.

Kathy Milligan - 1 year, 9 months ago

What is your opinion about buying books online? I think it's comfortable especially now according to the quarantine time. I prefer to use https://essaysworld.net/buy-a-book-review-essay. It's a service where you can get professional help with completing your assignments.

miranda splis - 7 months ago

Thank you! It helped me a lot!

Brenda Show - 6 months, 3 weeks ago
×

Problem Loading...

Note Loading...

Set Loading...