Reducing multinomial coefficients modulo a prime power

Robert J. Martin; Gary L. Mullen

doi:10.1016/0898-1221(84)90084-1

Reducing multinomial coefficients modulo a prime power

Robert J. Martin, Gary L. Mullen

Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

If p is a prime and l ≥ 1 then in Theorem 1 it is shown that the multinomial coefficient {A figure is presented} (mod p^l) if and only if {A figure is presented} where k^j_i is the residue of k_i mod p^j for j = 1, ..., h with h = [log k/log p] and [ ] is the greatest integer function. By comparing running times necessary to reduce randomly generated multinomial coefficients, this method is shown to be computationally faster than the previously known methods.

Original language	English (US)
Pages (from-to)	37-41
Number of pages	5
Journal	Computers and Mathematics with Applications
Volume	10
Issue number	1
DOIs	https://doi.org/10.1016/0898-1221(84)90084-1
State	Published - 1984

All Science Journal Classification (ASJC) codes

Modeling and Simulation
Computational Theory and Mathematics
Computational Mathematics

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10.1016/0898-1221(84)90084-1

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abstract = "If p is a prime and l ≥ 1 then in Theorem 1 it is shown that the multinomial coefficient {A figure is presented} (mod pl) if and only if {A figure is presented} where kji is the residue of ki mod pj for j = 1, ..., h with h = [log k/log p] and [ ] is the greatest integer function. By comparing running times necessary to reduce randomly generated multinomial coefficients, this method is shown to be computationally faster than the previously known methods.",

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AU - Mullen, Gary L.

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N2 - If p is a prime and l ≥ 1 then in Theorem 1 it is shown that the multinomial coefficient {A figure is presented} (mod pl) if and only if {A figure is presented} where kji is the residue of ki mod pj for j = 1, ..., h with h = [log k/log p] and [ ] is the greatest integer function. By comparing running times necessary to reduce randomly generated multinomial coefficients, this method is shown to be computationally faster than the previously known methods.

AB - If p is a prime and l ≥ 1 then in Theorem 1 it is shown that the multinomial coefficient {A figure is presented} (mod pl) if and only if {A figure is presented} where kji is the residue of ki mod pj for j = 1, ..., h with h = [log k/log p] and [ ] is the greatest integer function. By comparing running times necessary to reduce randomly generated multinomial coefficients, this method is shown to be computationally faster than the previously known methods.

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EP - 41

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

IS - 1

ER -

Reducing multinomial coefficients modulo a prime power

Abstract

All Science Journal Classification (ASJC) codes

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