2001 OIM Problems/Problem 1

Problem

We say that a natural number $n$ is "çharrúa" if it simultaneously satisfies the following conditions:

  • All digits of $n$ are greater than 1.
  • Whenever four digits of $n$ are multiplied, a divisor of $n$ is obtained.

Show that for each natural number $k$ there is a çharrúa number with more than $k$ digits.

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

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See also