Is there a way to compute the last digits of an arbitrarily large Fibonacci number?
For the $10^n$th Fibonacci number, we can just find the $2^n$-th Fibonacci number (if that isn't too large) $\bmod n$, and then use the Chinese remainder theorem, since we know it is a multiple of $5^n$ (the Pisano period is $4\cdot5^n$ which divides $10^n$) to find the last $n$ digits.
However, is there a way to find the last digits of the $n$-th Fibonacci number efficiently if $n$ is not a power of $10$?
A way to program this would probably require a way to reference the last two intermediate values and add them together, and then taking the result $\bmod 10^d$. Taking the value $\bmod 3\times10^d$ would be preferred because this allows the calculation to be iterated.