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.

For all positive integers x, a string of 3^(2+x) 3's is divisible by 3*3*3*3. Since the set of positive integers is infinite, there are an infinite number of numbers n that meet the two requirements.

Posted by Bryan on 2003-05-13 07:29:23