#1129 · Number Theory · Divisibility

Digit‑sum difference

Let $S_{1}$ be the sum of the decimal digits of a positive integer $N$ , and let $S_{2}$ be the sum of the decimal digits of $3 N$ . Prove that $S_{1} - S_{2}$ is a multiple of $3$ .

~5 minProof · checked by AIdigit summodular arithmetic

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. VII. Scales of Notation, Examples VII.b, No. 37

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