Math Forum

From: haoyuep@aol.com (Dan Hoey)
Date: Mar 7, 2002 8:47 AM
Subject: Re: generalized integer puzzle

The question of finding n for which
a_1 + a_2 + ... + a_n = a_1 . a_2 . ... . a_n
has exactly one solution in positive integers is addressed in R. K.
Guy, _Unsolved Problems in Number Theory, 2d ed_ under the heading
"Sum Equals Product."  I think it's item D28.

If I recall correctly, all such n under 50,000 or so are known (There
are fewer than ten.  Either 114 or 144 is one of them, and the other
has been published as a typo.) but it is not known whether there are
more.  I haven't looked to see if it seems likely there would be more,
but I tend to doubt it.

Dan