perplexus.info :: Numbers : Tetra-productial numbers

Tetra-productial numbers (Posted on 2003-05-13)

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: 2.2500 (4 votes)

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Puzzle Thoughts

Comment 7 of 7 |

(10^27- 1)/3 = 3333333333333333333333333 which is

divisible by 3*3*3*3= 81

We could vary the value of n , whenever (10^(27*n) -1)/27, and get an infinity of many integers satisfying the given conditions.

Posted by K Sengupta on 2023-05-02 23:43:29

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