2880 



Application of Trigonometry ; Cyclotomy 



2880 



Congruences, application of cyclotomy. 



Moesta, C. W. Grunert. Arch. 10 (1847) 98-. 

 , to divisors of cyclotomic functions. 



Hathaway, A. S. [1880] (xn) J. H. Un. 



Cir. [1] (1882) 67. 

 Congruent roots. Rummer, E. E. Crelle J. 



53 (1857) 142- . 

 Cyclotomic equations, irreducibility. Dedekind, 



E. Crelle J. 54 (1857) 27-. 

 , m prime, m-fold section. Glashan, J. C. 



Am. J. Mth. 21 (1899) 276-. 



, quinquisection. Glashan, J. C. [1897] 

 Am. J. Mth. 21 (1899) 270-. 



, theory. Migotti, A. [1882] Wien 

 Ak. Sb. 87 (1883) (Ab. 2) 7-. 



functions. Lucas, E. C. E. 90 (1880) 855-. 

 . Tanner, H. W. L. L. Mth. S. P. 20 



(1889) 63-, 258-. 



, considered with respect to prime 

 modulus p. Hathaway, A. S. [1881] (xn) 

 J. H. Un. Cir. [1] (1882) 131. 



, divisors. Sylvester, J. J. C. B. 90 

 (1880) 287-, 345-. 



, , Sylvester's theorem, proof. Pepin, T. 



C. E. 90 (1880) 526-. 

 Cyclotomy. Gauss, C. F. Par. S. Phlm. Bll. 



3 (1802) 102-. 

 . Frischauf, J. Wien Sb. 55 (1867) (Ab. 2) 



113-. 

 , application to theory of numbers. Jacobi, 



C. G. J. Berl. B. (1837) 127- ; Crelle J. 30 



(1846) 166- . 

 , (Jacobi). Lebesgue, V. A. 



Liouv. J. Mth. 19 (1854) 289-. 



derived from linear equations (for primes of 

 form 2 m + l). Hermes, J. [1878] Crelle 

 J. Mth. 87 (1879) 84-. 



, generalisation. Stickelberger, L. Mth. A. 



37 (1890) 321-. 

 , , algebraic. Berger, A. Stockh. 6fv. 



(1891) 683-; Fschr. Mth. (1891) 190-. 

 , new method. Quincke, G. A. Ps. C. 149 



(1873) 270-. 

 , primes of form 2 2 " + l. Lucas, E. C. E. 



85 (1877) 136-. 

 , proofs of theorems related to. Lanavicensis 



(Sylvester, J. J.). Ph. Mg. 18 (1859) 281-. 



by purely geometrical means ; possible cases. 

 Hessel, J. F. C. Grunert Arch. 37 (1861) 

 269-. 



Determinants arising in cyclotomy. Hermes, J. 



Arch. Mth. Ps. 6 (1888) 276-. 

 Divisibility of prime factor of class-number H 



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



396-. 

 Division of angle into 2 n + l equal parts. 



Kempe, A. N. Arch. Wisk. 1 (1895) 163- ; 



Fschr. Mth. (1893-94) 1152-. 



any number of equal parts. 

 Kempe, A. N. Arch. Wisk. 1 (1895) 215- ; 

 Fschr. Mth. (1893-94) 1153. 



Divisors of Fermatians. Sylvester, J, J. C. 



E. 106 (1888) 446-; Nt. 37 (1888) 417-. 

 form Ax 2 + By 2 + Cz 2 , proof of theorem of 



Lagrange, and divisors of functions which 



multisect the roots of unity. Sylvester, J. J. 



Am. J. Mth. 3 (1880) 390-. 



Divisors of functions of primitive roots of 

 unity. Sylvester, J. J. C. E. 92 (1881) 

 1084-. 



resulting from cyclotomy. Kummer, E. E. 

 Crelle J. 30 (1846) 107-. 



Equation for primitive roots of unity, irreduci- 

 bility. Lebesgue, V. A. Liouv. J. Mth. 4 

 (1859) 105-. 



nth roots of unity. Bang, A. S. N. 



Ts. Mth. 6 (B) (1895) 6-; Fschr. Mth. (1895) 

 121. 



t 2 -pu* = l, p prime, solution by circular 

 functions. Lejeune-Dirichlet, G. Crelle J. 

 17 (1837) 286-. 



a;p-i + p- 2 + . . . + 1 = is irreducible when 

 is prime. Kronecker, L. Crelle J. 



280; Liouv. J. Mth. 1 (1856) 399-. 



T- X=l + x+ ... + xP~ l = 0, p prime, irreduci- 

 bility. Prouhet, E. N. A. Mth. 9 (1850) 348-. 



Equations, resolubility, especially a; 71 -1=0. 

 Allegret, A. C. E. 43 (1856) 860-. 



Eulerian numbers, residues with respect to 

 prime modulus. Lucas, E . [1877] Par. 

 S. Mth. Bll. 6 (1878) 49-. 



Gauss, formula 



where 



Kronecker, L. Liouv. J. Mth. 1 (1856) 392-. 

 , theorem on 4 - , extension. Lucas, E. 



Tor. Ac. Sc. At. 13 (1877) 271-. 

 Gauss's sums. Seguier, de. C. E. 123 



(1896) 166-. 

 -- . Lerch, M. Casopis 28 (1899) 1- ; 



Fschr. Mth. (1898) 168. 

 -- , analogues. Lerch, M. Prag Sb. (1897) 



(Mth.-Nt.) No. 43, 16 pp. 



, series S e - . Mertens, F. Berl. 



Ak. Sb. (1896) 217-. 

 -- with several variables. Jordan, C. C. E. 



73 (1871) 1316-. 

 Imaginary cube roots. Horner,W.G. Thomson 



A. Ph. 8 (1816) 279-, 388-. 

 --- , every number has four. Lockhart, J. 



Thomson A. Ph. 5 (1815) 439-. 

 Eegular polygon, 17 sides, inscription. James, 



S. Ir. Ac. T. 13 (1818) 175-. 

 -- , -- , . Grunert, J. A. Arch. Mth. 



Ps. 42 (1864) 361-. 

 -- , -- , . Collignon, E. As. Fr. C. E. 



8 (1879) 162-. 



s, number of inscriptible. Dickson, 

 N. Y. Mth. S. Bll. 3 (1894) 123-. 

 -- ,7 and 13 sides, construction. Affolter, 



F. G. Mth. A. 6 (1873) 592-. 

 -- , 15 and 17 sides, inscription. Lebesgue, 



V. A. N. A. Mth. 5 (1846) 683-. 

 -- , 17 sides, construction. Staudt, G. K. 



C. von. Crelle J. 24 (1842) 251. 

 -- , -- , . Breton [de Champ], P. N. 



A. Mth. 5 (1846) 226-, 340. 

 -- , -- , . Houel, J. N. A. Mth. 16 



(1857) 310-. 



223 



