Cyclic Permutation of 3-Digit Multiple of 37

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Theorem

Let $n$ be a $3$-digit multiple of $37$.

Let $m$ be an integer formed by cyclically permuting the digits of $n$.

Then $m$ is also a multiple of $37$.

Proof

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Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $37$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $37$