2820 Quadratic residues 



125-. 



= c. Spelta, C. G. Mt. 33 (1895) 



^*^. Stfrmer, C. 



Christiania Skr. (Mth.-Nt. Kl.) (1895) No. 11, 



21pp. 

 u m + v n =iv k . Ermakov, V. [1898] Kec. Mth. 



(Moscou) 20 (1899) 293-. 

 A 1/1*1 MA . . . BN } Vi NJ>* ... = C. Stormer, C. 



C. B. 127 (1898) 752-. 

 2/ 2 = ax + 6. Besant, W. H. Mth. Gz. 1 (1900) 



130. 



2820 Quadratic residues. 



Gauss, C. F. Gott. Cm. 4 (1816-18) 3-. 

 Lebesgue, V. A. Liouv. J. Mth. 5 (1840) 186-. 

 Stern, M. A. Brux. Mm. Cour. 15 (1840-41) 



38 pp. 

 Scliaar, M. [1849-50] Brux. Ac. Sc. Mm. 



(1850) xxiv-. 

 Genocchi, A. Brux. Mm. Cour. 25 (1851-53) 



55 pp. 

 Stern, M. A. [1862] Crelle J. 61 (1863) 



334-. 

 Candida, Z. A. G. Teix. J. Sc. 1 (*1878) 



171-. 



Schering, E. Acta Mth. 1 (1882) 153-. 

 Nazimow, P. Bll. Sc. Mth. 9 (1885) 15-. 

 Buniakovskij, V. Ja. [1886] St Pet. Ac. Sc. 



Mm. (Rs.) 55 (1887) (SiijppZ.) No. 5, 16 pp. ; 



Fschr. Mth. (1887) 173. 

 Lipschitz, E. C. B. 108 (1889) 489-. 

 Matrot, A. As. Fr. C. B. (1890) (Pt. 2) 82-. 

 Frolov, M. As. Fr. C. B. (1892) (Pt. 2) 149-. 

 Eeich, K. Arch. Mth. Ps. 11 (1892) 176-, 



vn-. 



Pepin, . C. B. 128 (1899) 1553-. 

 Congruence 2 = c (mod. p*), resolution. To- 



nelli, A. Em. B. Ac. Line. Ed. 1 (1892) 



(Sem. 1) 116- ; 2 (1893) (Sent. 1) 259-. 

 Congruent division and quadratic residues. 



Stern, M. A. [1861] Crelle J. 61 (1863) 



66-. 

 Continued fractions and quadratic forms. La 



Vallee-Poussin, C. J. de. Brux. S. Sc. A. 19 



(1895) (Pt. 1) 111-. 

 Density of series of prime numbers. Konig, J. 



Mth. Nt. B. Ung. 14 (1898) 322. 

 Eisenstein's geometrical proof. Cayley,A. QJ. 



Mth. 1 (1857)- 186-. 

 Historical study. Pepin, T. Bm. N. Line. 



Mm. 16 (1899) 229-. 

 Prime modulus, square roots of unity for a. 



Tanner, H. W. L. Mess. Mth. 21 (1892) 



139-. 

 Problems on numbers (Fermat). Pepin, T. 



Bm. N. Line. Mm. 8 (1892) 85-. 

 Quadratic and cubic residues. Meyer, G. Arch. 



Mth. Ps. 63 (1879) 1-. 



reciprocity, formula of Gauss, extension. 

 Le Besgue, V. A. C. B. 59 (1864) 1067-. 



residue-character. Gegenbauer, L. Wien 

 Ak. Sb. 100 (1891) (Ab. 2a) 1072-. 



, determination. Schering, E. Gott. 



Ab. 24 (1879) (Mth.) 47 pp. 



Quadratic residues 2820 



Quadratic residue-character, determination by 



continued fractions. Zeller, C. Gott. Nr. 



(1879) 197-. 

 , Gauss's criterion. Schering, E. Berl. 



Ak. Mb. (1876) 330-. 

 , . Kronecker, L. Berl. Ak. Mb. 



(1876) 331-. 

 of number 2. Stieltjes, T. J. (jun.) 



N. Arch. Wisk. 9 (1882) 193- ; Toul. Fac. 



Sc. A. 11 (1897) A, 4 pp. 

 3 for any prime. Bricard, E. 



N. A. Mth. 16 (1897) 546-. 



residues and non-residues. Cauchy, A. L. 

 C. E. 10 (1840) 437-. 



. Lebesgue, V. A. Liouv. J. 



Mth. 7 (1842) 137-. 

 of a prime, distribution. Aladov, 



N. S. Bee. Mth. (Moscou) 18 (1896) 61-; 



Fschr. Mth. (1896) 146. 

 , . Sterneck, E. von. 



[1898] Eec. Mth. (Moscou) 20 (1899) 269- ; 



Fschr. Mth. (1898) 153-. 

 primes, combination. Bounia- 



kowsky, V. [18681 St Pet. Ac. Sc. Bll. 13 



(1869) 25-. 

 , periods and primitive roots. Arndt, C. F. 



Grunert Arch. 2 (1842) 1-. 

 of primes of form 4m + 3. Woronoj, G. F. 



Fschr. Mth. (1899) 184. 

 , trigonal, and bitrigonal residues. Stern, 



M. A. [1869] Crelle J. 71 (1870) 137-. 

 Eeciprocity law. Eisenstein, G. Crelle J. 28 



(1844) 41-. 

 . Liouville, J. Liouv. J. Mth. 12 (1847) 



95-. 



. Mansion, P. Mess. Mth. 5 (1876) 140-. 



. Petersen, J. P. C. (xn) Ts. Mth. 3 



(1879) 86- ; (x) Am. J. Mth. 2 (1879) 285-. 



. Kronecker, L. Bll. Sc. Mth. As. 4 



(1880) 182-. 



. Sylvester, J. J. C. B. 90 (1880) 1053-, 



1104-. 

 _ _. Gegenbauer, L. Wien Ak. Sb. 90 



(1885) (Ab. 2) 1026- ; 97 (1889) (Ab. 2a) 427-. 

 . Kronecker, L. Crelle J. Mth. 104 (1889) 



348-. 

 . Lucas, E. St Pet. Ac. Sc. Bll. 33 (1890) 



495-. 

 . Gegenbauer, L. Wien Ak. Sb. 103 (1894) 



(Ab. 2a) 285-. 

 . Uasenohrl, F. Wien Az. 31 (1894) 



74-. 

 . Kmiig, G. Mth. Term. Ets. 13 (1895) 



429- ; Acta Mth. 22 (1899) 181-. 



for complex numbers. Lejeune-Dirich- 

 let, G. Crelle J. 9 (1832) 379-. 



and Gauss's sums. Mertens, F. Wien 



Ak. Sb. 103 (1894) (Ab. 2o) 1005-. 

 , history. Kronecker, L. Berl. Ak. Mb. 



(1875) 267-. 

 , Legendre's, extension. Jenkins, M. [1867] 



L. Mth. S. P. 2 (1869) 29-. 

 , , to numbers not prime. Genocchi, 



A. C. E. 90 (1880) 300-. 



, , and Gauss's sums. Sochocki, J. 

 Par. T. Nauk Sc. Pam. 10 (*1878) Art. 1, 

 37 pp. ; Fschr. Mth. (*1878) 315. 



204 



