Theorem on the Binomial Coefficient for Positive Real Number
نویسندگان
چکیده
منابع مشابه
IMPROVED BOUNDS ON THE NUMBER OF WAYS OF EXPRESSING t AS A BINOMIAL COEFFICIENT
Let N(t) denote the number of ways of writing t as a binomial coefficient. We show that N(t) = O ( (log t)(log log log t) (log log t)3 ) .
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For a prime p and nonnegative integers n, k, consider the set A (p) n,k = {x ∈ [0, 1, ..., n] : p|| ( n x ) }. Let the expansion of n + 1 in base p be n + 1 = α0p ν + α1p ν−1 + · · · + αν , where 0 ≤ αi ≤ p − 1, i = 0, . . . , ν. Then n is called a binomial coefficient predictor in base p(p-BCP), if |A (p) n,k| = αkp , k = 0, 1, . . . , ν. We give a full description of the p-BCP’s in every base p.
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Let us note that every non empty loop structure which is add-left-cancelable and add-rightcancelable is also add-cancelable and every non empty loop structure which is add-cancelable is also add-left-cancelable and add-right-cancelable. Let us note that every non empty loop structure which is Abelian and add-right-cancelable is also add-left-cancelable and every non empty loop structure which i...
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ژورنال
عنوان ژورنال: Social Science Research Network
سال: 2023
ISSN: ['1556-5068']
DOI: https://doi.org/10.2139/ssrn.4378490