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- Feb 14, 2012

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Find the smallest value of $n$ for which $\dfrac{n!\cdot n!}{(n+6)!}$ is an integer.

- Thread starter anemone
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- Thread starter
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- #1

- Feb 14, 2012

- 3,941

Find the smallest value of $n$ for which $\dfrac{n!\cdot n!}{(n+6)!}$ is an integer.

- Mar 31, 2013

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89Find the smallest value of $n$ for which $\dfrac{n!\cdot n!}{(n+6)!}$ is an integer.

90 = 9 * 10

91 = 13 * 7

92 = 23 * 4

93 = 3 * 31

94 = 2 * 47

95 = 5 * 19

take the product and we have 10 different numbers < 90 on the right and product divided 89!

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- #3

- Feb 14, 2012

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Well done,89

90 = 9 * 10

91 = 13 * 7

92 = 23 * 4

93 = 3 * 31

94 = 2 * 47

95 = 5 * 19

take the product and we have 10 different numbers < 90 on the right and product divided 89!