Question about A001175, period of Fibonacci mod n

[T. D. Noe]

This sequence, http://www.research.att.com/projects/OEIS?Anum=A001175, has
a comment saying that "Dan Asimov observed and Victor Miller proved that
for p prime, a(p^k) = p^(k-1)*a(p)".  Does anyone have a reference for
this?  D. D. Wall, in his 1960 paper, proved this result assuming that a(p)
does not equal a(p^2).  Are there more recent results?

Thanks,

Tony