I am not sure if I am approaching the problem below in the right way. Is there any chance that someone can check it for me,please?
Show that the equation
I assumed by contradiction that is an integer solution to our problem and it has the smallest value of of any such solution.
We can also note that is in fact a Pythagoran triple as .
for some co-prime integers . Let be even and be odd, but that also imlpies that either or is divisible by . Hence contradict the fact that they are integer.