Perhaps this article provides a proof:
Blakley, G. R.; Borosh, I. Modular arithmetic of iterated powers. Comput. Math. Appl. 9 (1983), no. 4, 567--581.
Review of Zentralblatt:
http://www.zentralblatt-math.org/zmath/e...t=complete
Blakley, G. R.; Borosh, I. Modular arithmetic of iterated powers. Comput. Math. Appl. 9 (1983), no. 4, 567--581.
Review of Zentralblatt:
http://www.zentralblatt-math.org/zmath/e...t=complete
