#1127 · Number Theory · Divisibility

Digit‑rearrangement difference

Let $N$ be a number written in base $r$ . Form a new number $N^{'}$ by permuting the digits of $N$ in any order. Show that $N - N^{'}$ is always divisible by $r - 1$ .

~6 minProof · checked by AIdigital summodular arithmetic

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. VII. Scales of Notation, Examples VII.b, No. 35

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