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# There is a magic number, around 6 digits long (I can't remember exactly) and when you add, multiply, subtract and divide parts of it (or something like that) it does amazing stuff. Sorry I can't be more specific, I don't remember myself. What is this number?

Question #80295. Asked by auccl799. (May 12 07 8:19 PM)

gmackematix

It is difficult to know quite what you are looking for with that description.
The 6-digit cyclic number 142,857 is quite unusual in that:
142,857 x 2 = 285,714
142,857 x 3 = 428,571
142,857 x 4 = 571,428
142,857 x 5 = 714,285
142,857 x 6 = 857,142
142,857 x 7 = 999,999
Also 142 + 857 = 999.
The square of 142,857 = 20,408,122,449 and...
20,408 + 122,449 = 142,857.

All these facts relate to it being the recurring part of 1/7 as a decimal, but I'll let you find out why...

 May 12 07, 8:44 PM

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