[math-fun] Wilson's theorem on primes (no, not that one, the one about decimals)

rcs at xmission.com rcs at xmission.com David Wilson and Warren Smith batted about the side puzzle: When can the reciprocal of a composite N contain every digit combination of length floor[log10(N)]? Smith (roughly) argued 'never', and Wilson pointed out that some prime powers worked. Adding a bit more fuel: The reciprocals of 343 (7^3), 841 (29^2), and 799 (17*47) each contain all two-digit combinations. Rich

--plainly, I was wrong. But why?