#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

Stuck? A gentle nudge

Something off?

Workspace

Your working

Check your full solution

Attach photos of your pages (up to 3) or one PDF — or check what you typed above. Lemma reads the work and verifies the reasoning, not just the answer.

Your first check today doesn't need an account.

Your photos and PDFs are read once and not stored — only the transcription is kept.