2001 OIM Problems/Problem 1

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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$ (Error compiling LaTeX. Unknown error_msg)k$there is a ''çharrúa'' number with more than$ (Error compiling LaTeX. Unknown error_msg)k$ digits.

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

Solution

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See also