Determine all possible pair(s) (X, Y), with X being a prime and Y being a positive integer, that satisfy this equation:

(X-1)! + 1 = X^Y

(In reply to Very little progress to report by Harry)

I had got as far as the equation in your fourth graf, and no farther, but your reference to Hardy sent me looking around.

I found this mathworld link http://mathworld.wolfram.com/WilsonPrime.html which mentions that the search has been extended to  <IMG class=inlineformula height=17 alt=5×10^8 src="http://mathworld.wolfram.com/images/equations/WilsonPrime/Inline2.gif" width=40 border=0> with no other solutions found.  That's enough for me. 

 

Posted by xdog on 2009-04-24 17:52:57