Problem 1176

Show that any number of the form $2^{4 n+2}+1$ can be easily factored by the use of the identity $4 x^{4}+1=\left(2 x^{2}+2 x+1\right)\left(2 x^{2}-2 x+1\right)$. Factor $2^{18}+1$ using this identity.