251252253254⋮≡25≡625≡625≡625⋮(mod1000)(mod1000)(mod1000)(mod1000)⋮
We know that the last 3 digits of 25n will always be a constant 625 for large enough integer values of n.
What is the smallest positive integer value a such that the last 5 digits of (5a)n will always be a constant for large enough integer values of n?