Period of Reciprocal of 43 is Odd

Theorem

The decimal expansion of the reciprocal of $43$ has an odd period, that is, $21$:

$\dfrac 1 {43} = 0 \cdotp \dot 02325 \, 58139 \, 53488 \, 37209 \, \dot 3$

Proof

From Reciprocal of $43$:

$\dfrac 1 {43} = 0 \cdotp \dot 02325 \, 58139 \, 53488 \, 37209 \, \dot 3$

Counting the digits, it is seen that this has a period of recurrence of $21$.

Hence the result.

$\blacksquare$