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- November 29th 2011, 12:15 PM #1

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## a!b! = a! + b! + c!

This is a BMO 1 question from 2003 that has me completely stumped.

Any help on basic operations on factorials would be appreciated as I have no idea how they can be manipulated.

Thanks.

EDIT:

Apogies, I forgot to state that all possible values of a b and c are to be found

- November 29th 2011, 12:40 PM #2

- November 29th 2011, 11:57 PM #3

- November 30th 2011, 12:52 AM #4

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## Re: a!b! = a! + b! + c!

A quick thought (I don't know if it's useful). You can try independent looking at the possible orderings of {a,b,c}. For example, what happens if ? We can safely assume that because of the symmetry in the equation.

With them being ordered, you will know how much you can "divide out" (sorry, don't know the English word) and where.

- November 30th 2011, 08:09 AM #5

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- November 30th 2011, 08:16 AM #6

- November 30th 2011, 09:20 AM #7

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