2850 Congruences other than Linear ; Cubic and Higher Residues 2850 



Cubic and biquadratic residues. Stieltjes, T. J. 



(jun.) Amst. Ak. Vs. M. 17 (1882) 338-; Arch. 



Neerl. 18 (1883) 358-. 

 with respect to prime modulus.. 



Pellet, A. E. Par. S. Mth. Bll. 10 (1882) 



157-. 



other residues with respect to prime 

 modulus. Lucas, E. As. Fr. C. B. (1886) 

 (Pt. 2) 101-. 



residues. Jacobi, C. G. J. Crelle J. 2 

 (1827) 66-. 



. Kummer, E. E. Crelle J. 23 (1842) 



285-; 32 (1846) 341-. 



. Meyer, G. F. Arch. Mth. Ps. 43 (1865) 



413-. 



. Pepin, T. C. K. 79 (1874) 1403- ; 



Liouv. J. Mth. 2 (1876) 313-. 



Decomposition of numbers, Format's proposi- 

 tions, extension. Bealis, S. N. A. Mth. 5 

 (1886) 113-. 



Determinantal congruences to prime modulus. 

 Sardi, C. G. Mt. 5 (1867) 371-. 



Divisibility of periodic numbers and determina- 

 tion of decimal periods. Barillari, G. [1870] 

 G. Mt. 9 (1871) 125-. 



Divisors of functions of primitive roots of unity. 

 Sylvester, J. J. C. E. 92 (1881) 1084-. 



Format's theorem, generalisation. Dickson, 

 L. E. A. Mth. 1 (1900) 31-. 



, x* (m) = 1 (mod. m), generalisation. 

 Lucas, E. C. E. 84 (1877) 439-. 



, ( ). Picquet, H. C. E. 96 



(1883) 1136-, 1424. 

 , ( ), . Lucas, E. C. E. 96- (1883) 



1300-. 

 , _ (_), _. Pellet, A. E. C. E. 96 



(1883) 1301-. 

 , ( ), . Kantor, S. C. E. 96 (1883) 



1423. 

 , ( ), . Grandi, A. Ven. I. At. 



1 (1883) 809-. 

 , ( ), . Cardane, G. Ev. Mt. 5 



(1895) 25-. 

 , ( ), . Dickson, L. E. C. E. 128 



(1899) 1083-. 

 , ( ), theorem resembling. Horner, 



W. G. _Ph. Mg. 11 (1837) 456-. 

 , a p ~ 1 = l (mod. p) first demonstration. 



Vacca, G. Bb. Mth. (1894) 46-. 



, ( ), generalisation. Koenigs, G. 

 Bll. Sc. Mth. As. 8 (1884) 286-. 



, ( ), pew demonstration. Garibaldi, 



C. G. Mt. 26 (1888) 197-. 



Functions irreducible with respect to prime 

 modulus. Pellet, [A.] E. C. E. 70 (1870) 

 328- ; 90 (1880) 1339- ; 93 (1881) 1065-. 



reduced with respect to prime modulus. 

 Pellet, A. E. Par. S. Mth. Bll. 17 (1889) 



Higher reciprocity, function connected with. 



Stern, M. A. Crelle J. 55 (1858) 193-. 

 Indices appertaining to given number. Laisant, 



C. A. Bordeaux S. Sc. Mm. 1 (1876) 



400-. 



with complex modulus. Hill, C. J. D. 

 Lund Acta Un. 1 (1864) (Mth.) No. 6, 18 pp. ; 

 Crelle J. 70 (1869) 282-. 



216 



Integral functions irreducible with respect to a 

 prime modulus, when degree is equal to 

 modulus. Serret, J. A. Liouv. J. Mth. 18 

 (1873) 301-. 



, power of 



modulus. Serret, J. A. Liouv. J. Mth. 18 

 (1873) 437-. 



Integrals, any order, residues. Marie, M. C. 



E. 75 (1872) 1475-. 

 , double, Cauchy's method extended to. 



Marie, M. C. E. 75 (1872) 865-, 937-; Par. 



EC. Pol. J. 27 (=Cah. 44) (1874) 51-. 

 Irreducible congruences. Dickson, L. E. N. Y. 



Am. Mth. S. Bll. 3 (1897) 381-. 

 , Eisenstein's theorems. Sch&nemann, T. 



Crelle J. 40 (1850) 185-. 

 Period-length of decimal corresponding to 1/p, p 



being one of first 1500 primes. Kessler, E. 



Arch. Mth. Ps. 3 (1886) 99-. 



lengths of circulates. Cunningham, (Lt.- 

 Col.) A. Mess. Mth. 29 (1900) 145-. 



Periods of circulating decimals, method of 



forming. Johnson, W. W. Mess. Mth. 14 



(1885) 14-. 

 pure circulates, frequency of occurrence 



of digits. Reynolds, B. Mess. Mth. 27 



(1898) 177-. 

 Polynomials, application in theory of numbers. 



Crelle, A. L. Berl. Ab. (1843) 49-. 

 Power residues. Skrivan, G. Wien Jbr. Ober- 



Eealsch. Inn. Stadt 3 (1861) 1-. 

 . Jonquieres, de. C. E. 124 (1897) 



334-, 428. 



of complex numbers. Kronecker, L. 

 Berl. Ak. Mb. (1880) 404-. 



numbers for composite modulus. 

 Bennett, G. T. [1892] Phil. Trans. (A) 184 

 (1894) 189-. 



, proof of double theorem, and extension 



of idea of congruence. Hofmann, F. Mth. 



A. 20 (1882) 471-. 

 , theory. Zsigmondy, K. Mh. Mth. Ps. 



3 (1892) 265-. 

 Prime numbers, property connected with Fer- 



mat's theorem. Sylvester, J. J. C. E. 52 



(1861) 161-, 212-, 307-. 



.theorems. Froth, F. C. E. 87 (1878) 926. 



of which a given number cannot be a 



primitive root. Jonquieres, de. C. E. 



123 (1896) 405-. 

 Primitive roots. Murphy, R. Ph. Mg. 19 



(1841) 369. 

 . Frolov, . Par. S. Mth. Bll. 21 



(1893) 113- ; 22 (1894) 241-. 

 , comparative number. Szily, K. Mth. 



Termt. Ets. 9 (1891) 264-; 10 (1882) 19-; 



Mag. Tud. Ak. Ets. 2 (1891) 478. 

 of congruence XP~ } = 1 (mod. p). Kefer- 



stein, H. Hamb. Mth. Gs. Mt. 1 (1889) 256-. 

 for odd prime modulus. Perott, J. Bll. 



Sc. Mth. 17 (1893) 66- ; 18 (1894) 64-. 

 or its power. Perott, J. 



Bll. Sc. Mth. 9 (1885) 21-. 



, period, Jacobi 's formation, proof. Le 

 Besgue, V. A. C. E. 70 (1870) 1243-. 



of primes of certain type. Wertheim, G. 



Acta Mth. 20 (1897) 143-. 



