RMO Rules

Prove that when \((x+1)^{n}\) is divided by \((x-1)^{3}\). The remainder is \[n\left( n-1 \right) \left( { 2 }^{ n-3 } \right) \left( { x }^{ 2 } \right) -{ 2 }^{ n-2 }x\left( { n }^{ 2 }-3n \right) +{ 2 }^{ n-3 }\left( { n }^{ 2 }-5n+8 \right) \]

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}`	\( \boxed{123} \)

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 6 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

RMO Rules

Comments

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.