×

# On the treatise of determining co-primes.

$$gcd(k,p)=1$$

The formula states:

$${ k }^{ p\quad }\equiv \quad k-p\quad (mod\quad p)$$

$$k>p$$

For example:

Using $$2$$ as $$p$$,

And knowing that $$k=3$$

$${ 3 }^{ 2 }\quad \equiv \quad 1\quad (mod\quad 2)$$

By trying out other primes, this always work.

However, one link is still missing can we solve this equation by only knowing $$p$$?

Note by Luke Zhang
2 years, 9 months ago

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. 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 1paragraph 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} $$\boxed{123}$$

Sort by:

It doesnt only work for primes, it works for some other numbers too, but I'm not sure how to generalize it

- 2 years, 9 months ago

This has been proven using Fermat's Little theorem. But how do I validate it?

- 2 years, 9 months ago

Did u proof that it would work for all primes and only primes?

And how did u find time during CNY?

- 2 years, 9 months ago