Q:

Expressing any given number in the form of $x^y + y^x$

I was told by one of my friends that any given positive integer can be expressed in the form of $x^y + y^x$ where x & y are integers.
For example: 17 = $2^3+3^2$
Surprisingly,this could be done for any number. Now he gave me some another number (like 23421) and asked me to find out the values of x & y.
I racked my brain but couldn't get it. Can any one please explain, how is this possible
and how to get the values of x & y

A:

It is a joke problem ("spoiler" below).
$$ $$
The joke is that if $x > 1$ and $y > 1$ the set of  integers of the form $x^y + y^x$ has density zero, so that most numbers are not expressible, while if $x=1$ is allowed the problem is trivial.  Hence the misdirection.

