Zobrazeno 1 - 10
of 21
pro vyhledávání: '"Joseph B. Muskat"'
Publikováno v:
International Journal of Mathematics and Mathematical Sciences, Vol 9, Iss 4, Pp 665-704 (1986)
For primes p≡4, 11(mod15) explicit formulae are obtained for the cyclotomic numbers of order 15 over GF(p2).
Externí odkaz:
https://doaj.org/article/aa9cfd6b2fa144509b79f67e41b24f33
Publikováno v:
Acta Arithmetica. 70:215-278
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::ae5c561211c405731ab98ed15f459b04
https://doi.org/10.4064/aa-70-3-215-278
https://doi.org/10.4064/aa-70-3-215-278
Autor:
Joseph B. Muskat
Publikováno v:
Mathematics of Computation. 61:365-372
Consider the sequences { u n } \{ {u_n}\} and { v n } \{ {v_n}\} generated by u n + 1 = p u n − q u n − 1 {u_{n + 1}} = p{u_n} - q{u_{n - 1}} and v n + 1 = p v n − q v n − 1 , n ≥ 1 {v_{n + 1}} = p{v_n} - q{v_{n - 1}},n \geq 1 , where u 0 =
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::a9a6a10b8d89135b13f1f29ad0583435
https://doi.org/10.1090/s0025-5718-1993-1192974-3
https://doi.org/10.1090/s0025-5718-1993-1192974-3
Publikováno v:
Mathematics of Computation. 55:327-343
We give a deterministic algorithm for finding all primitive representations of a natural number n in the form f u 2 + g v 2 f{u^2} + g{v^2} , where f and g are given positive coprime integers, and n ≥ f + g + 1 n \geq f + g + 1 , ( n , f g ) = 1 (n
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::5f6e04ca8043ce846a4e6bdf9ea395e2
https://doi.org/10.1090/s0025-5718-1990-1023762-3
https://doi.org/10.1090/s0025-5718-1990-1023762-3
Publikováno v:
Mathematics of Computation. 55:327
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::651ba84b4962429ac7a1b4c4b729af0d
https://doi.org/10.2307/2008809
https://doi.org/10.2307/2008809
Autor:
Yun Cheng Zee, Joseph B. Muskat
Publikováno v:
Proceedings of the American Mathematical Society. 49:13-19
An arithmetic proof by L. E. Dickson of the uniqueness of the integral solutions of a certain quaternary quadratic form is generalized to include several similar forms which have appeared recently in cyclotomy. In his exposition of cyclotomy of order
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::6c246ba2797065eb55f8e3592a4739c0
https://doi.org/10.1090/s0002-9939-1975-0360461-9
https://doi.org/10.1090/s0002-9939-1975-0360461-9
Publikováno v:
International Journal of Mathematics and Mathematical Sciences. 9:665-704
For primesp≡4,11(mod15)explicit formulae are obtained for the cyclotomic numbers of order15overGF(p2).
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::8f1c353ffa8016497dd343b4e02ef786
https://doi.org/10.1155/s0161171286000832
https://doi.org/10.1155/s0161171286000832
Autor:
Joseph B. Muskat
Publikováno v:
Journal of Number Theory. 19:263-282
Let p ≡ ± 1 (mod 8) be a prime which is a quadratic residue modulo 7. Then p = M2 + 7N2, and knowing M and N makes it possible to “predict” whether p = A2 + 14B2 is solvable or p = 7C2 + 2D2 is solvable. More generally, let q and r be distinct
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5cb3c006914c5e0029e617df153bd2b3
https://doi.org/10.1016/0022-314x(84)90111-2
https://doi.org/10.1016/0022-314x(84)90111-2
Autor:
Joseph B. Muskat
Publikováno v:
Acta Arithmetica. 11:263-279
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::6ec06d0a6f108b80afa6c022b952725b
https://doi.org/10.4064/aa-11-3-263-279
https://doi.org/10.4064/aa-11-3-263-279
Autor:
Joseph B. Muskat
Publikováno v:
Canadian Journal of Mathematics. 16:343-352
Lower case italics will denote rational integers, while lower case Greek letters will denote algebraic integers. The Law of Quadratic Reciprocity can be formulated as follows:If p and a are distinct odd primes, then a is a quadratic residue (mod p) i
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::bf7dae606e21ab040b1086806fa81cad
https://doi.org/10.4153/cjm-1964-034-5
https://doi.org/10.4153/cjm-1964-034-5