# Number Theory Proof

Let $$n\geqslant 2$$ and $$k$$ be any positive integers. Prove that $$(n-1)^2 | (n^k - 1)$$ if and only if $$(n-1) | k$$.

Note by أحمد الحلاق
1 year, 7 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:

Just use the identity

$$\frac{n^k-1}{n-1}=n^{k-1}+\ldots+n^1+1$$

and take the resulting equation $$\text{mod n}$$

- 1 year, 7 months ago

Thank you so much

- 1 year, 7 months ago

I mean $$\text{mod (n-1)}$$

- 1 year, 7 months ago

Could you please provide a solution?

- 1 year, 7 months ago