I did try to proof this by contradiction(I guess it works). So I suppose this statement is false but I have confused about the meaning of it.

If this statment is false it means “There are odd integers x,y,z according to $(x-z)^2$ + $(y-z)^2$ = $(x+y)^2$.” or “There are odd integers x,y,z according to $(x-z)^2$ + $(y-z)^2$ $neq$ $(x+y)^2$.” or…..

Is proof by contradiction a good method? and Could you help me how to do next from the statement that suppose to be false?

Thank you very much.