# Prove them! (part 1)

Prove them if you can!

Whatever it's easy or not, I hope that you can try to prove the problems below. Sadly, I can't prove them... Try your best and please post your proof below and state what method/theorem etc. did you use.

1) Prove that the sum of two odd square numbers is always not divisible by 4.

2) Prove that any triangle can be cut into six similar triangles. (Your proof must be valid for all triangles and not just a specific type. )

Don't forget to write the question number when posting your proof.There are more problems! Wait for the next note!. Thanks for proving...!

.

Note by Brilliant Member
4 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:

First I will write a proof of the first, its easy though. Let the two odd square numbers be $$(2n+1)^2$$ and $$(2k+1)^2$$. Now, on adding them, we get $$(2n+1)^2+(2k+1)^2=4n^2+4n+1+4k^2+4k+1$$ Which is $$4(n^2+k^2+n+k)+2$$, which clearly leaves a remainder of 2 when divided by 4.

- 4 years ago

Thanks!

- 4 years ago

How about the first question? Anyone proved it?

- 3 years, 12 months ago