Hardest Math Problem in the World || International Linguistics Olympiad || Math Olympiad || 

Mr white 17 is prime need not have too many equations, consecutive nos are solutions, square of the nos, required exponents are, the final solutions, these are all atsite,mental, vedic one line solutions , please refer vedics, u will come to know Mukund

х=3, у=4

Hmmmm... What you do from (2:10) onwards would only be justified if the expressions x^y and y^x would be restricted to integers. There was no such statement in the problem presentation at the beginning. And i do not see any acknowledgement of that boundary condition afterwards... In fact, if we allow any - including real, maybe even complex - numbers, as was stated in the problem presentation (where no realm restriction at all was given), we arrive at infinitely many solutions, since for every x there can be found a fitting y that satisfies the presented equation. We don't have an underdefined equation system here for no reason. With two variables and only one equation, we have one degree of freedom left.