In this answer, the author says each block of $n\times m$ elements is split into $\gcd(m,n)$ distinct cycles. This seems nontrivial, how is this proven?
2026-03-25 17:22:23.1774459343
Greatest Common Divisor in pair of cycles
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HINT: $$ \gcd(m,n)=\dfrac{m\times n}{\operatorname{lcm}(m, n)} $$