Lower bound: $m/\gcd(m,\ell-1) - 1 \le S_m(k,\ell)$ once $k \ge n-1$ · Prove2Me

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Lower bound: $m/\gcd(m,\ell-1) - 1 \le S_m(k,\ell)$ once $k \ge n-1$ · Prove2Me