Road to IMO!

Congratulations to one of the most brilliant young minds in the Brilliant community for passing the PMO Area Stage Qualifiers - @Sean Anderson Ty. I say that this is a great feat for there are many who had the chance but wasn't able to qualify (Yep, I'm talking about me) He also lives/studies in the same city as I am, so I am proud that maybe one of ours is going to be part of IMO. As a gift, I give these Fibonacci problems (Who doesn't like proving?) 1) Let $m$ and $n$ be positive integers. Prove that, if $m$ is divisible by $n$ , then, $f_{m}$ is divisible by $f_{n}$ . 2) Let $m$ and $n$ be positive integers whose greatest common divisor is $d$ . Prove that the greatest common divisor of the Fibonacci numbers $f_{m}$ and $f_{n}$ is the Fibonacci number $f_{d}$

Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

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Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
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Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1 paragraph 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"

Math	Appears 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

@Sean Ty

Marc Vince Casimiro - 6 years, 6 months ago

@Sean Ty Congrats!

Calvin Lin Staff - 6 years, 6 months ago

Math	Appears 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}`	$\boxed{123}$