Solution for "That's something interesting!"

https://brilliant.org/problems/thats-something-interesting/?group=j0gXDzTOQ64o

Given: a!b! = a!+b! a>0; b>0; Solution: Factorial definition (http://en.wikipedia.org/wiki/Factorial) is a!=1234...a Let's assume a>b, so b!=a!(a+1)(a+2)(a+3)...b or b!=a!x, where x>1 Next a!b! = a!+b! => ${ (a!) }^{ 2 }$ x = (a!)(1+x) => x= $\frac { 1 }{ a!-1 }$ .
x will never be greater than 1. Therefore, a=b => ${ (a!) }^{ 2 }$ = 2(a!) => a! = 2 => a = 2, b = 2, a+b = 4

#NumberTheory #Factorial

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FYI You can enter your solution directly on the problem. After you solved it, and clicked on reveal solutions, you will see:

Calvin Lin Staff - 6 years, 4 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}`	$\boxed{123}$