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Problem Solving (PS) | Re: The value of ((8!) + (9!))^2 is an integer. What is the greatest in

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andrewjohn8 wrote:

Thought I'd add my solution since I believe I didn't see it anywhere.

I factored out the Sqrt(8!) first.

(sqrt(8!(1 + sqrt(9))^2

which reduces to

((sqrt(8!)*(4))^2

8!*16

Then to do the same method as others have shown to get that there are 7 factors of 2 in 8! plus the 4 factors of 2 in 16 means there are at most 11 factors of 2.­


That’s good stuff! Very clever

Posted from my mobile device

Statistics : Posted by DanTheGMATMan • on 17 Aug 2023, 03:00 • Replies 14 • Views 13807



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