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# KCC's Quizzes AQQ242 about equation with embedded factorial

I think most of us are now back from their summer vacations! Thus brains are fully recharged!

This following challenge should not be difficult to solve...

Good luck!

P.S. If you think there are colleagues who can be interested in our weekly quizzes, please forward them the site (https://ez.analog.com/how-to-use-engineerzone/logic-lounge/)

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## Top Replies

• Bravo Rajesh! you have found the solutions, congratulations!

• Bravo Gaetano, you used the right method to find the solutions, congratulations!

• It's n=2 or n=3.

• Bingo Dmitry, you get it! Congratulations!

• Let's publish now the official and detailed answers:

The equation can be developed as:

n (n²-1) = (n+1)!

n (n-1) (n+1) = (n+1) n (n-1) (n-2).. 1

n (n-1) = n (n-1) (n-2).. 1

1 = (n-2)!

Hence: n=2 and n=3 are the 2 solutions

Congratulation to all the ones having solved the equation and big applause for our 4 first winners:

(from USA),  (from Canada),  (from India) and  (from Turkey)

Be prepared for the next coming challenge!

• n^3-n=(n+1)!

n(n+1)(n-1)=(n+1)n(n-1)(n-2)....

1=(n-2)!

Two solutions: n=2 because 0!=1 and n=3 because 1!=1

• Correct  , that's the strange fact that both 0! and 1! give both the same result of 1 It can be demonstrated by using the Gamma function in which the factorial is a subset....