#1131 · Number Theory · Divisibility
Parity of digit sum in odd radix
In a numeral system whose base (radix) is odd, prove that the sum of the digits of any number has the same parity as the number itself: the digit sum is odd when the number is odd, and even when the number is even.
H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. VII. Scales of Notation, Examples VII.b, No. 39
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