Multiplicative polynomials and Fermat's little theorem for non-primes
Fermat's Little Theorem states that xp=x(modp) for x∈N and prime p, and so identifies an integer-valued polynomial (IVP) gp(x)=(xp−x)/p. Presented here are IVP's gn for non-prime n that complete the sequence {gn|n∈N} in a natural way. Also presented are characterizations of the gn's a...
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| Format: | Article |
| Language: | English |
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Wiley
1997-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171297000719 |
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| _version_ | 1832561718902915072 |
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| author | Paul Milnes C. Stanley-Albarda |
| author_facet | Paul Milnes C. Stanley-Albarda |
| author_sort | Paul Milnes |
| collection | DOAJ |
| description | Fermat's Little Theorem states that xp=x(modp) for x∈N and prime
p, and so identifies an integer-valued polynomial (IVP) gp(x)=(xp−x)/p. Presented here
are IVP's gn for non-prime n that complete the sequence {gn|n∈N} in a natural way.
Also presented are characterizations of the gn's and an indication of the ideas from topological
dynamics and algebra that brought these matters to our attention. |
| format | Article |
| id | doaj-art-90064731b1954e89830b8670673e849b |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1997-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-90064731b1954e89830b8670673e849b2025-02-03T01:24:27ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251997-01-0120352152810.1155/S0161171297000719Multiplicative polynomials and Fermat's little theorem for non-primesPaul Milnes0C. Stanley-Albarda1Department of Mathematics, University of Western Ontario, Ontario, London N6A 5B7, CanadaDepartment of Mathematics, University of Toronto, Ontario, Toronto M5S 1A1, CanadaFermat's Little Theorem states that xp=x(modp) for x∈N and prime p, and so identifies an integer-valued polynomial (IVP) gp(x)=(xp−x)/p. Presented here are IVP's gn for non-prime n that complete the sequence {gn|n∈N} in a natural way. Also presented are characterizations of the gn's and an indication of the ideas from topological dynamics and algebra that brought these matters to our attention.http://dx.doi.org/10.1155/S0161171297000719Fermat's little theoremmultiplicative function polynomials. |
| spellingShingle | Paul Milnes C. Stanley-Albarda Multiplicative polynomials and Fermat's little theorem for non-primes International Journal of Mathematics and Mathematical Sciences Fermat's little theorem multiplicative function polynomials. |
| title | Multiplicative polynomials and Fermat's little theorem for non-primes |
| title_full | Multiplicative polynomials and Fermat's little theorem for non-primes |
| title_fullStr | Multiplicative polynomials and Fermat's little theorem for non-primes |
| title_full_unstemmed | Multiplicative polynomials and Fermat's little theorem for non-primes |
| title_short | Multiplicative polynomials and Fermat's little theorem for non-primes |
| title_sort | multiplicative polynomials and fermat s little theorem for non primes |
| topic | Fermat's little theorem multiplicative function polynomials. |
| url | http://dx.doi.org/10.1155/S0161171297000719 |
| work_keys_str_mv | AT paulmilnes multiplicativepolynomialsandfermatslittletheoremfornonprimes AT cstanleyalbarda multiplicativepolynomialsandfermatslittletheoremfornonprimes |