×

# Maybe IMO should give this out

Prove that there does exist some integers $$n$$ such that $$3^{n}+3^{n-1}+3^{n-2}+......+3^{4}+3^{3}+3^{2}+3^{1}+3^{0}$$ is a perfect square, or else define the $\color{BLUE}{\huge{1000th}}$ smallest value of $$n$$.

Note by Bryan Lee Shi Yang
2 years, 10 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} $$\boxed{123}$$

## Comments

Sort by:

Top Newest

...Sorry, note edited.

- 2 years, 10 months ago

Log in to reply

You have mentioned it to be an integer. Other values will be 0,1,4

- 2 years, 10 months ago

Log in to reply

I am sorry, it should be a $$POSITIVE$$ number.

- 2 years, 10 months ago

Log in to reply

It can be a perfect square. Smallest possible value of n will be -1.

- 2 years, 10 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...