There're a couple more "magic" numbers: 0 and 1. :)

>1) Take a three-digit number (example: 317). Repeat it, to get a six-digit number (example: 317317). Divide it by 7 (you will get no remainder!). Divide the result by 11 (no remainder!). Now, divide the result by 13 (again, no remainder. Also, you get the original number back, example: 317).
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>2) Take the "magic number" 142857. Multiply it by several integers, e.g.:
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>142857 x 2 =
>142857 x 3 =
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>The results are quite interesting; for factors 2-6, you get all the digits of the original number, but in a different sequence.
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>Hilmar.