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 = $2^3+3^2$...--prophetes.ai

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

It is a joke problem ("spoiler" below).

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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.