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Tetra-productial numbers (Posted on 2003-05-13) Difficulty: 3 of 5
Show that there are infinitely many integers n such that:

1) All digits of n in base 10 are strictly greater than 1.
2) If you take the product of any 4 digits of n, then it divides n.

See The Solution Submitted by Fernando    
Rating: 1.3333 (3 votes)

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Solution | Comment 2 of 6 |
(10^27-1)/3 is a number which fits the conditions of the problem. (10^27-1)/3 = 333333333333333333333333333 which is a multiple of 3*3*3*3.

An infinite sequence can be made using (10^(27*n)-1)/3
  Posted by Brian Smith on 2003-05-13 08:03:13
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