2850 Congruences other than Linear ; Cubic and Higher Residues 2850 



Biquadratic residue-character of number two. 



Lejeune-Dirichlet, G. [1857] Crelle J. 57 



(1860) 187-. 

 . Halphen, G. C. E. 66 



(1868) 190-. 



residues. Gauss, C. F. Gott. Cm. 6 (1823- 

 27) 27-; 7 (1828-31)89-. 



. Mathieu, E. Liouv. J. Mth. 12 (1867) 



377-. 

 . Stieltjes, T. J. (jun.) Bll. Sc. Mth. 



As. 7 (1883) (Ft. 1) 139-. 



, fundamental theorem. Eisenstein, G. 

 Crelle J. 28 (1844) 223-. 



"Canon arithmeticus," Jacobi's, note. Le- 

 besgue, V. A. C. E. 39 (1854) 1069- . 



Circulating decimal, number of figures in period. 

 Contejean, L. Par. S. Phlm. Bll. 4 (1892) 



decimals and Fermat's theorem. Genese, 

 R. W. B. A. Ep. (1888) 580-. 



, rule of remainders. Goodwyn, H. 

 (vi Adds.) Nicholson J. 1 (1802) 314-. 



, theory. Brogtrop, A. J. M. N. Arch. 



Wisk. 3 (*1877) 58-. 

 Congruence, condition for existence of definite 



number of roots. Gegenbauer, L. Wien Ak. 



Sb. 95 (1887) (Ab. 2) 165-. 



of Fermat. Gruber, N. Mth. Termt. Ets. 

 14 (1896) 22-; Mth. Nt. B. Ung. 13 (1897) 

 413-. 



prime modulus. Piuma, C. M. A. Mt. 



11 (1882-83) 237-. 

 , 3rd degree. Ivanov, I. St Pet. Ac. Sc. 



Bll. 5 (1896) 137- ; Fschr. Mth. (1896) 149. 

 , , with simple modulus, number of 



roots. Woronoj, G. T. Fschr. Mth. (1898) 



156. 

 , 4th degree, with prime modulus. Cordone, 



G. Palermo Cir. Mt. Ed. 9 (1895) 209-. 



= a (mod. p). Stern, . Crelle J. 



Mth. 100 (1887) 182-. 



2 n -a7/ n = (mod. M), resolution. Dick- 

 stein, S. [1892] Krk. Ak. (Mt.-Prz.) Ez. 6 

 (1893) 155- ; Crc. Ac. Sc. Bll. (1892) 372-. 



x 11 + A 1 x n ~ l + A^c n ~ 2 + ... +.4 n = (mod. p), 

 resolution. Snopek, E. Prace Mt.-Fiz. 4 

 (1893) 63-; Fschr. Mth. (1893-94) 289. 



x m =b (mod. 2"), resolution. Amid, N. 

 Palermo Cir. Mt. Ed. 8 (1894) 187-. 



- 2 4 = (-) (2n) \l(n !) 2 where 2n + 1 is a prime. 

 Morley, F. A. Mth. 9 (1894-95) 168-. 



2 X = E (mod. p, mod. m). Cunningham, 

 (Lt.-Col.) A. B. A. Ep. (1895) 613. 



(r p-1 1) : p'=q r (mod. p). Mirimanqff, D. 

 Crelle J. Mth. 115 (1895) 295-. 



a;* = 6 (mod. p*), resolution. Amid, N. 

 Palermo Cir. Mt. Ed. 11 (1897) 43-. 



#p-' - 1 = (mod. p z ), upper limit of number 

 of roots. Aladow. J. S. Fschr. Mth. (1899) 

 185. 



Congruences. Eaussnitz, G. (xn) Mth. Term. 



Ets. 1 (1883) 296-; Mth. Nt. B. Ung. 1 



(1882-83) 266-. 

 . Gegenbauer, L. Wien Ak. Sb. 95 (1887) 



(Ab. 2) 610-. 



Congruences. Demeczky, M. Mth. Termt. 



Ets. 7 (1889) 131- ; Mth. Nt. B. Ung. 8 



(1891) 51-. 

 . Gegenbauer, L. Wien Ak. Sb. 98 (1890) 



(Ab. 2a) 652-. 

 . Eogel, F. Arch. Mth. Ps. 10 (1891) 84-. 



and application to indeterminate analysis. 

 Bie, L. H. (xn) Ts. Mth. 2 (1878) 

 161-. 



cubic residues. Stern, M. A. Crelle J. 9 



(1832) 97-. 

 , employment of roots in theory of numbers. 



Cauchy, A. L. C. E. 25 (1847) 37-. 



and equations, similarity between, and its 

 significance. Hathaway, A. S. [1880] (xn) 

 J. H. Un. Cir. [1] (1882) 97. 



having no roots with respect to prime 

 modulus. Zsigmondy, K. [1894] D. Mth. 

 Vr. Jbr. 4 (1897) 109- ; Mh. Mth. Ps. 8 

 (1897) 1-. 



, modulus p n where p is prime. Schonemann, 



T. Crelle J. 32 (1846) 93-. 

 , number of figures in periods of reciprocals 



of integers. Muir, T. Mess. Mth. 4 (1875) 



, roots. Gegenbauer, L. Wien Ak. 



Sb. 102 (1893) (Ab. 2a) 549-. 



and residues. Arndt, F. Grunert Arch. 6 

 (1845) 380-. 



, resolution of class. Pellet, A. E. C. E. 88 



(1879) 417-. 

 , , logarithmic tables for various moduli. 



Bellavitis, G. Em. E. Ac. Line. T. 1 (1877) 



778-. 

 - with respect to prime modulus. ScJwnemann, 



T. Crelle J. 31 (1846) 269-. 

 . Stankevich, B. V. [1882] 



(xn) Eec. Mth. (Moscou) 10 (1882-83) (Ft. 1) 



112-. 

 -. Gegenbauer, L. Mh. Mth. 



Ps. 5 (1894) 230-. 

 , and to irreducible modular 



function. Serret, J. A. Par. Ac. Sc. Mm. 



35 (1866) 617-. 

 , resultant of two. Sylvester, J. J. [1881] 



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



with several variables. Gegenbauer, L. Wien 

 Ak. Sb. 99 (1891) (Ab. 2a) 790-. 



, theorems. Poinsot, L. [1817-18] Par. 



Mm. de PL (1813-15) 381- ; Par. Mm. Ac. 



Sc. 4 (1819-20) 99-. 

 , . Libri, G. [1825] Par. Mm. Sav. Etr. 



5 (1838) 1-. 

 , . Cauchy, A. L. [1829-31] Ferussac 



Bll. Sc. Mth. 12 (1829) 205- ; 15 (1831) 137-; 



Par. Mm. Ac. Sc. 17 (1840) 249-. 

 , . Galois, E. Ferussac Bll. Sc. Mth. 13 



(1830) 428-. 

 , . Stern, M. A. Crelle J. 12 (1834) 



288-. 

 , . Cauchy, A. L. C. E. 44 (1857) 



77- 



in a; of ith order with prescribed number of 

 roots. Zsigmondy, K. Wien Ak. Sb. 103 

 (1894) (Ab. 2a) 135-. 



Cubic and biquadratic characters. Pellet, A. E. 

 C. E. 108 (1889) 609-. 



215 



