Help: finding materials to study coprime numbers

Hello, everybody.

My teacher recently (a year ago) gave me some sheets with problems about coprime numbers, however, without help I couldn't solve even one problem. It is quite sad because I usually don't feel so beat down by math that I wouldn't even get an idea of where to start with solving a problem. That got me thinking that perhaps I lack understanding of coprimes. Perhaps anyone know great resources for learning some stuff about them? Keep in mind that I am not really advanced in math and that all things about coprimes that I know are that greatest common divisor of all the coprime numbers are 1 (recently got into phi function as well, but that is not helping me at all in doing those problems :( ).

Examples of problems that I am struggling with:

1: Prove that if aa and bb are coprime, then ama^m and bmb^m are also coprime, if mm is any natural number.

2: Prove that if aa is a prime number, which isn't equal to 2 nor 3, then a21a^2 - 1 is a multiple of 24. (Oh, I think that I lack of understanding of prime numbers as well)

And quite a lot more. (I understand when someone give the solution to problem, but I can't grasp any of them on my own...)

If you don't know any books, but can give me some advice, I would be glad to read it :)

Note by Zyberg Nee
3 years, 5 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} ai1 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 sinθ \sin \theta
\boxed{123} 123 \boxed{123}

Comments

Sort by:

Top Newest

First example: As gcd(a,b)=1\gcd(a,b)=1, a and b have no common prime factors. They won't have any common prime factors when they are raised to a natural number. The result follows.

Second example: All prime numbers>3 are of the form 6n±16n \pm 1 where n is a positive integer.

So, a21=36n2±12n=12n(3n±1)a^2-1=36n^2 \pm 12n=12n(3n \pm 1).

If n is even, 24 all divide 12n and if n is odd, 24 will divide 12(3n±1)12(3n \pm1).

Proved.

A Former Brilliant Member - 3 years, 5 months ago

Log in to reply

Check out greatest common divisor and euclidean algorithm.

Calvin Lin Staff - 3 years, 5 months ago

Log in to reply

Thank you very much!

Zyberg NEE - 3 years, 5 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...