Prime and prime power divisibility of Catalan numbers
Citations
107 citations
Cites background or methods from "Prime and prime power divisibility ..."
...Note that not only have we been able to determine the length and starting and ending points of the block (which was also done by Alter and Kubota) but our demonstration is combinatorial as opposed to the original proof of Theorem 5.1 which is arithmetic....
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...Alter and Kubota [4] have generalized this result to arbitrary primes and prime powers....
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...The divisibility of the Catalan numbers Cn = 1 n + 1 ( 2n n ) , n ∈ N, by primes and prime powers has been completely determined by Alter and Kubota [4] using arithmetic techniques....
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..., n ∈ N, by primes and prime powers has been completely determined by Alter and Kubota [4] using arithmetic techniques....
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...Theorem 5.1 (Alter and Kubota) Let p ≥ 3 be a prime and let q = (p + 1)/2....
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Cites background from "Prime and prime power divisibility ..."
...On the other hand, the studies on the congruences of the Motzkin numbers Mn are few and were energized very recently....
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...There are many ways to define Mn , but in order to calculate the congruences, we choose the above definition....
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Cites background from "Prime and prime power divisibility ..."
...The reader will find in [1] information about the prime decomposition of Catalan numbers and [21] describes divisibility by 2 of the Stirling numbers of second kind....
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References
43 citations