Period of Reciprocal of 19 is of Maximal Length

Theorem
The decimal expansion of the reciprocal of $19$ has the maximum period, that is: $18$:
 * $\dfrac 1 {19} = 0 \cdotp \dot 05263 \, 15789 \, 47368 \, 42 \dot 1$

Proof
Performing the calculation using long division:

0.05263157894736842105... 19)1.00000000000000000000000    95    152     76      --    ---     --      50    180     40      38    171     38      --    ---     --      120     90     20      114     76     19      ---     --     --        60    140     100        57    133      95        --    ---     ---         30     70    ...         19     57         --     --         110    130          95    114          --    ---          150    160          133    152           --    ---           170     80           152     76