2880 



Application of Trigonometry ; Cyclotomy 



2880 



Primary prime functions. Hancock, H. [1900] 

 N. Y. Am. Mth. S. Bll. 7 (1901) 202, 206-. 



Prime factor of class-number H, divisibility 

 by X. Kronecker, L. Liouv. J. Mth. 1 (1856) 

 39&-. 



factors of .certain forms, Lejeune-Dirichlet's 

 theorems. Kronecker, L. Berl. Ak. Sb. 

 (1888) 417-. 



ideals in relation to substitution groups. 

 Frobenius, G. Berl. Ak. Sb. (1896) 689-. 



, separation of number-field into. Hilbert, 



D. Mth. A. 44 (1894) 1-. 



integral complex numbers formed from fourth 

 roots of unity. Gegenbauer, L. Wien Ak. Sb. 

 101 (1892) (Ab. 2a) 984-. 



Primes and prime ideals in domain of fifth 

 roots of unity. Gmeiner, J. A. Mh. Mth. 

 Ps. 11 (1900) 1-. 



Primitive factors of 4 (1 -a-)/(l -x), reduc- 

 tion of product to form Y-^nZ 2 , Cauchy's 

 theorem. Genocchi,A. C. E. 67 (1868) 1035-. 



Quadratic complex numbers, certain systems. 

 Western, A. E. [1898] Camb. Ph. S. T. 17 

 (1899) 109-. 



Kepresentation of numbers of a class-domain. 

 Hensel, K. Crelle J. Mth. 103 (1888) 230-. 



by forms. Poincare, H. C. E. 92 



(1881) 777- ; Par. S. Mth. Bll. 13 (1885) 162-. 



. Gegenbauer, L. Wien Ak. Sb. 



95 (1887) (Ab. 2) 618-. 



Symmetric matrices. Kronecker, L. Berl. Ak. 

 Sb. (1889) 349-. 



2880 Application of trigonometri- 

 cal functions to arithmetic; 

 cyclotomy. 



Absolutely smallest residues of real magnitudes. 

 Kronecker, L. Berl. Ak. Sb, (1885) 383-, 

 1045-. 



Arithmetical series, Dirichlet's theorem. Syl- 

 vester, J. J. As. Fr. C. B. (1888) (Pt. 2) 

 118. 



Binomial equations. 



Liouville, J. Liouv. J. Mth. 2 (1857) 413-. 

 Trudi, N. [1866] Nap. At. Ac. 3 (1866-68) 



No. 6, 49 pp. 



Rubini, R. G. Mt. 5 (1867) 184-. 

 and algebraic .radicals. Valat, . Bordeaux 



Act. Ac. Sc. (1843) 321-. 

 alternating sums formed with primitive roots. 



Cauchy, A. L. C. K. 10 (1840) 560-. 

 application of Sturm's theorem. Gascheau, G. 



Liouv. J. Mth. 7 (1842) 126-. 

 to summation of series. Berger,A. Ups. S. 



Sc. N. Acta 13 (1887) No. 7, 36 pp. 

 depression of degree. Lobatschewsky, N. (vi 



Adds.) Kazan Mm. Un. (1834) 1-. 

 existence and characteristics of roots. Meray, 



C. Par. EC. Norm. A. 2 (1885) 337-. 

 functions of roots. Schlmemann, T. Crelle J. 



17 (1837) 372-. 

 irreducibility. Mertens, F. Wien Ak. Sb. 99 



(1891) (Ab. 2a) 907-. 



, 



(1832) 

 -M -1 = 



reducibility. Bucca, F. Palermo Cir. Mt. Ed. 



14 (1900) 136-. 



reducible. Vahlen, K. Acta Mth. 19 (1895) 195-. 

 roots. Tardy, P. A. Mt. 3 (1869-70) 331-. 

 , extraction. Berkhout, J. J. T. van (\i Adds.) 



Arch. Wisk. Gn. 1 (1859) 54-. 

 solution. Gamier, J. G. Brux. Ac. Bll. 6 



(1839) 474-. 

 , cases. Lentheric, . Gergonne A. Mth. 



21 (1830-31) 101-. 

 , trigonometric. Tetmajer, J. (XH) Krk. 



Ak. (Mt.-Prz.) Pam. 5 (1880) 117-. 

 sums of powers of a primitive root. Cauchy, 



A. L. C. E. 10 (1840) 594-. 

 transformations. Gram, J. P. Ts. Mth. 5 



(1887) 44-; Fschr. Mth. (1887) 72-. 

 z 257 =l, solution. Richelot, F. J. Crelle J. 9 

 1-, 146-, 209-, 337-. 

 = 0, solution. Fischer, P. A. Crelle J. 



11 (1834) 201-. 



xP = l. Lebesgue, V. A. C. E. 5 (1837) 722-. 

 A B =C. Pagani, G. M. Brux. Ac. Bll. 4 



(1837) 387; Brux. Ac. Sc. Mm. 11 (1838) 



11 pp. 

 ,-c m -l = 0, trigonometric series derived from. 



Cauchy, A. L. C. E. 10 (1840) 719-. 

 xP-l = 0, p prime, solution. Realis, S. N. 



A. Mth. 2 (1843) 5-, 147-. 

 xP=l, auxiliary equation of mth order 



(p=mTr + l). Lebesgue, V. A. C. E. 18 



(1844) 696-. 



x p -1 = 0, modular indices of polynomials con- 

 nected with. Cauchy, A. L. C. E. 25 (1847) 



93-. 

 XP - 1 = 0, p prime, solution. Plana, G. [1850] 



Tor. Mm. Ac. 11 (1851) 413-. 

 a: 257 -1 = 0. Cayley, A. Crelle J. 41 (1851) 



81. 

 x n -l = 0, primitive roots. Lebesgue, V. A. 



N. A. Mth. 11 (1852) 417-. 

 zP=l, Lagrange's resolvent, expression ana- 

 logous to. Kummer, E. E. Em. At. 6 



(1852-53) 237-. 

 x*>=l, p prime, solution. Lebesgue, V. A. 



C. E. 38 (1854) 914-. 

 w n =l, periods formed by roots when n is not 



prime. Fuchs, L. [1862] Crelle J. 61 (1863) 



374-. 

 x m -l = Q. Catalan, E. C. Brux. Ac. Bll. 29 



(1870) 182-. 

 x p - 1 = 0, trisection and quartisection. Cayley, 



A. L. Mth. S. P. 11 (1879-80) 4-. 

 a;**- 1 = 0, quinquisection. Cayley, A. L. 



Mth. S. P. 12 (1880-81) 15- ; 16 (1884-85) 



xf- 1 = 0. Scott, C. A. Am. J. Mth. 8 (1886) 



261-. 

 a^" 1 = 0, quinquisection. Tanner, H. W. L. 



L. Mth. S. P. 18 (1886-87) 214-. 

 a;** -1 = 0, p prime, solution. Butters, J. W. 



Edinb. Mth. S. P. 7 (1889) 10-. 

 a; 17 -1=0. Cayley, A. Mess. Mth. 19 (1890) 



184-. 

 a;P-l = 0, solution. Pierpont, J. N. Y. Am. 



Mth. S. Bll. 2 (1896) 77-. 

 a: 71 1 = 0, solution. Jarollmek, V. fiasopis 



27 (1898) 209- ; Fschr. Mth. (1898) 75. 



222 



