Period of Reciprocal of 17 is of Maximal Length

Theorem
The decimal expansion of the reciprocal of $17$ has the maximum period, that is: $16$:
 * $\dfrac 1 {17} = 0 \cdotp \dot 05882 \, 35294 \, 11764 \, \dot 7$

Proof
Performing the calculation using long division:

0.058823529411764705... 17)1.000000000000000000000    85      68     --      --         150      20             136      17     ---      --      140      30      136      17      ---      --        40     130        34     119        --     ---         60     110         51     102         --     ---          90      80          85      68          --      --           50     120           34     119           --     ---           160      100           153       85           ---      ---             70     ...             68