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.
(In reply to
Solution by DJ)
On second thought, the digits don't even need to be 9s. Twos, threes, whatever, any string of like digits with 8i digits will work. 9s just occurred to me first.
For example:
33333333=3333*10001
Also, the number of digits can be any multiple of 4, not just multiples of 8.
555555555555=5555*100010001
22222222222222222222=2222*10001000100010001
and so on.
What I said before is still true, but it does not have to be so specific. I don't know how to do a formal proof for the problem, but this is the general form of the/a solution.
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Posted by DJ
on 2003-05-14 06:57:05 |
re[fined]: Solution
