What are the possible remainders whenFn(thenth Fermat numberFn:= 2^2n+ 1,

n¸1) is divided by (a). 3, (b). 7, (c). 9?

I know the Fermat number is defined as 2^(2n)+1, but have trouble in finding possible remainders.

Like I can find F_0=2^0+1=2, so remainder when dived by 3 is 1, 5 when divided by 7, 7 when divided by 9

I guess I could continue in this method, but might there be an easier way to do this?