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 on Mar 24, 2005 at 10:01 UTC ( #442002=note: print w/replies, xml ) Need Help??

If I'm not mistaken, N! | NN, as N! = 1*2*...*N, and NN = N*N*...*N. Therefore, NN/N! = NN-1/(N-1)!
The fact that NN and N! share a factor doesn't mean that N! is a divisor of NN, as the following table shows:
``` N                 NN                 N!             NN % N!
1                  1                  1                  0
2                  4                  2                  0
3                 27                  6                  3
4                256                 24                 16
5               3125                120                  5
6              46656                720                576
7             823543               5040               2023
8           16777216              40320               4096
9          387420489             362880             227529
10        10000000000            3628800            2656000
11       285311670611           39916800           26301011
12      8916100448256          479001600          443667456
13    302875106592253         6227020800         5268921853
14  11112006825558016        87178291200          294332416
15 437893890380859375      1307674368000       820814907375
```

Replies are listed 'Best First'.
by QM (Parson) on Mar 24, 2005 at 19:58 UTC
My bad. Somehow the coffee fairy didn't stop by me, and I'm confusing "share a factor" with "evenly divides".

-QM
--
Quantum Mechanics: The dreams stuff is made of

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