×

# Divisibility example.

If $$d|n$$ then prove that $${ 2 }^{ d }-1|{ 2 }^{ n }-1$$.

This is my solution

If $$d|n$$ then $$n=dk$$ for some $$k$$.Then we have to prove $${ 2 }^{ d }-1|{ 2 }^{ dn }-1$$ or $${ 2 }^{ d }-1|{ ({ 2 }^{ d }) }^{ k }-1$$.Now let $$x={ 2 }^{ d }$$ therefore we have to prove $$x-1|{ x }^{ k }-1$$ which is true by Remainder theorem.

Note by Shivamani Patil
3 years 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:

NICE but too EASY.

- 3 years ago

Math is neither easy nor difficult for her lover.@Krishna Ar

- 3 years ago

haha

- 3 years ago

- 3 years ago

- 3 years ago

nice....

- 3 years ago