# Need help 2

$\gcd \left( a+b, \dfrac{a^p+b^p}{a+b}\right) = 1 \text{ or } p$

If $$p$$ is an odd prime and $$a,b$$ are co-prime positive integers, prove the equation above.

Note by Akshat Sharda
2 years, 2 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:

- 2 years, 2 months ago

- 2 years, 2 months ago

Nice one Akshat !!! @Akshat Sharda

- 2 years, 2 months ago

Just an outline since I'm at work: You can write $$\frac{a^p+b^p}{a+b}=pa^{p-1}+(a+b)q(a,b)$$ for some polynomial $$q$$ (simple algebra exercise). Thus a common divisor of $$\frac{a^p+b^p}{a+b}$$ and $$a+b$$ is also a divisor of $$pa^{p-1}$$, which proves our point.

- 2 years, 2 months ago

Exactly !!!DId the same !

- 2 years, 2 months ago