Open Problem Garden

we need to show A(pwr)x+B(pwr)y != C(pwr)z to disprove it. let us take A(pwr)x+B(pwr)y where A is an odd no. and B is an even no. and x,y>=3 then apply power to A(odd number) gives an odd number apply power to B (even number) gives an even number OR ELSE let us take A(pwr)x=2n+1 B(pwr)y=2n the addition of Ax+By gives an odd number =>2n+1+2n =4n+1……(1) where n€odd numbers.substitute odd number in (1),we get an odd number which cannot be shown as a number’s power the result must be a constan