Let n be a positive integer. If a == (3^{2n}+4)^-1 mod(9), what is the remainder when a is divided by 9?

Go online and use this Inverse Calculator: https://planetcalc.com/3311/

 

Enter "a" as an "integer". No matter what "n" you choose, it will always be an EVEN power of 3 and will not make any difference in the answer. Enter 9 under "modulo".

For example: a == (3^{2n}+4)^-1=(3^{2*3}+4 =3^6+4 =729 + 4 =733. Enter this under "integer" and press "calculate".