What is the cheapest and fastest way to find the remainder of the modular arithmetic $\pmod {n}$ when we have the reminder for $\pmod {n-1}$ or $\pmod {n+1}$ ?
As an example, if:
$$ 3^{60} \equiv 128433\pmod {2^{20}} $$
then
$$ 3^{60} \equiv ?\pmod {2^{20}+1} $$