The number nine in base ten enjoys some nice arithmetic properties. In this paper, we show that these properties are not intrinsic to the number nine; in fact, they are true for the largest digit in any base b. Four properties involving the final sums of all the digits of a number in a non-decimal base are explored and proofs of these properties are given in the appendix.
Goel, Sudhir and Simons, Kathy
"Properties Enjoyed by the Highest Digit in a Base Other than the Base 10,"
Georgia Journal of Science, Vol. 67, No. 2, Article 4.
Available at: https://digitalcommons.gaacademy.org/gjs/vol67/iss2/4