The calculations you described are wrong. If a is a multiple of 7 (or 13 or 19), then (a^6)^144 = (0^6)^144 = 0 mod 7. We can confirm this (using python): >>

The calculations you described are wrong. If a is a multiple of 7 (or 13 or 19), then (a^6)^144 = (0^6)^144 = 0 mod 7. We can confirm this (using python): >>> (7864)%1729 742L