On divisibility concerning binomial coefficients

Let k and n be positive integers. We mainly show that $(l n + 1) ∣ k (\binom{k n + l n}{k n}),$ $2 (\binom{k n}{n}) ∣ (\binom{2 n}{n}) C_{2 n}^{(k - 1)},$ $(\binom{k n}{n}) ∣ (2 k - 1) C_{n} (\binom{2 k n}{2 n}),$ $(\binom{2 n}{n}) ∣ (k + 1) C_{n}^{(k - 1)} (\binom{2 k n}{k n}),$ $2^{k - 1} (\binom{2 n}{n}) ∣ (\binom{2 (2^{k} - 1) n}{(2^{k} - 1) n}) C_{n}^{(2^{k} - 2)},$ $(6 n + 1) (\binom{5 n}{n}) ∣ (\binom{3 n - 1}{n - 1}) C_{3 n}^{(4)},$ and $(\binom{3 n}{n}) ∣ (\binom{5 n - 1}{n - 1}) C_{5 n}^{(2)},$ where C_n denotes the Catalan number $(\binom{2 n}{n}) / (n + 1)$ , and C_m^{(h)} refers to the Catalan number $(\binom{(h + 1) m}{m}) / (h m + 1)$ of order h.

On divisibility concerning binomial coefficients

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On divisibility concerning binomial coefficients

文献摘要

讨论

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On divisibility concerning binomial coefficients

文献摘要

讨论

|讲解博客

|AI智能校验

On divisibility concerning binomial coefficients

文献摘要

讨论

|讲解博客

|AI智能校验

讲解博客

AI智能校验

讲解博客

AI智能校验