2830 Quadratic binary forms 



Pellian equation. Aubel, H. van. As. Fr. C. 



E. (1885) (Pt. 2) 135-. 

 . Frattini, G. G. Mt. 33 (1895) 371- ; 



34 (1896) 98-. 

 and connected problems. Oettinger, L. 



Arch. Mth. Ps. 49 (1869) 193-. 

 , and connexion with rational triangles. 



Muller, E. Arch. Mth. Ps. 5 (1887) 111-. 

 , correction of error in Barlow. Martin, 



Art. Des Moines Anal. 2 (1875) 140-. 

 , extension of Degen's tables. Brit. Ass. 



Comm. (Cayley). B. A. Bp. (1893) 73-. 

 , property. Meyer, A. Zur. Vjschr. 32 



(1887) 363-. 

 , . Stflrmer, C. N. Ts. Mth. 7 (B) 



(1896) 49-; Fschr. Mth. (1896) 166. 

 and quadratic binary forms of positive 



determinant. Smith, H. J. S. L. Mth. S. 



P. 7 (1875-76) 196-. 

 , solution. Luce, J. B. Silliman J. 8 



(1849) 55-. 

 , . Minnigerode, B. Gott. Nr. (1873) 



619-. 

 , by elliptic functions. Kronecker, L. 



Berl. Mb. (1863) 44-. 

 , theorems. Lejeune-Dirichlet, G. Berl. 



Ab. (1834) 648-. 

 , - (Dirichlet). Tarn, F. Crelle J. Mth. 



105 (1889) 160-. 



, . Stfrmer, C. Christiania Skr. 

 (Mth. Nt. Kl.) (1897) No. 2, 48 pp. 



Pell's equation y*-3x z = l. Boutin, A. Mathesis 



18 (1898) 159-. 

 Prime factors of numbers of form l + 4x 2 . 



Markov, A. St Pet. Ac. Sc. Bll. 3 (1895) 



55-; Fschr. Mth. (1895) 201. 

 A+x*. Ivanov, I. St Pet. 



Ac. Sc. Bll. 3 (1895) 361- ; Fschr. Mth. 



(1895) 201. 



number 4n + 1 is sum of two squares. Her- 

 mite, C. N. A. Mth. 12 (1853) 45-. 



. Gopel,A. N. A. Mth. 



12 (1853) 136-, 170-. 

 . Harmuth, T. Arch. 



Mth. Ps. 66 (1881) 327-. 

 . Realis, S. N. A. 



Mth. 4 (1885) 367-. 



. Bock,J.W. Hamb. 



Mth. Gs. Mt. 1 (1889) 101-. 



numbers expressible by mx 2 + ny*. Euler, L. 

 [1778] St Pet. Ac. Sc. N. Acta 12 (1801) 



of form A 2 + \B* (B being odd). Liou- 



ville, J. Liouv. J. Mth. 10 (1865) 281-, 285-, 



289-, 293-, 295-. 

 4^ 2 + 5 2 (A being odd). Liouville, 



J. Liouv. J. Mth. 11 (1866) 41-. v 

 m 2 +fcn 2 . Kiipper, K. Casopis 10 



(*1881) 10-; Fschr. Mth. (1881) 135. 



as sum of two squares. Harmuth, T. 

 [1881] Arch. Mth. Ps. 67 (1882) 215-. 



Primitive forms, whose minus determinant is 



>0 and =3 (mod. 8). Liouville, J. Liouv. 



J. Mth. 11 (1866) 191-. 

 Problem. Miller, T. H. Edinb. Mth. S. P. 9 



(1891) 23-. 

 Pythagorean numbers, generalisation. Ziige, 



. Arch. Mth. Ps. 17 (1900) 354-. 



Other quadratic forms 2840 



Quadratic forms and certain ' ' greatest integer ' ' 

 formulae. Lerch, M. Prag fieske" Ak. Fr. 

 Jos. Bz. (Tfida 2) 7 (1898) Art. 7, 8 pp. ; Prag 

 Fr. Jos. Ac. Sc. Bll. (Mth. Nt.) 5 (1898) 33-. 



-- giving primes. Oltramare, G. Gen. I. 

 Nt. Mm. 5 (1857) (pte. 2) 1-. 



-- and special automorphic groups. Fricke, 

 R. Mth. A. 39 (1891) 62-. 



moduli, forms. Young, J. R. Ph. Mg. 33 

 (1848) 45-. 



Eeduction. Hurwitz, A. Mth. A. 45 (1894) 

 85-. 



, continual. Picard, E. C. K. 96 (1883) 

 1779-. 



SerieS Z Asymptotic value. 



Mertens, F. Wien Ak. Sb. 106 (1897) (Ab. 2a) 



Sums of squares equal to a square, method of 



finding. Euler, L. St P6t. Ac. Sc. Mm. 11 



(1830) 12-. 

 Theorem of Dirichlet. Cayley, A. Camb. and 



Dubl. Mth. J. 9 (1854) 163-. 

 --- . Meyer, A. Crelle J. Mth. 103 (1888) 



98-. 

 --- . Mertens, F. Wien Ak. Sb. 109 (1900) 



(Ab. 2a) 415-. 

 Gauss, demonstration. Perott, J. de. 



[1889] J. H. Un. Cir. [9 (1889-90)] 30. 



2840 Quadratic forms of three 

 or more variables; bilinear 

 forms. (See also 2060, 2070.) 



Bouniakowsky, V. [1849] St Pet. Ac. Sc. Mm. 



7 (1853) 303 -. 

 Arndt, F. Grunert Arch. 13 (1849) 105-, 410- ; 



15 (1850) 429-. 



Hermite, C. Crelle J. 47 (1854) 313-, 343-. 

 Liouville, J. Liouv. J. Mth. 2 (1857) 424. 

 Lipschitz, R. Crelle J. 54 (1857) 193-. 

 Hermite, C. C. B. 55 (1862) 684-. 

 Skrivan, G. Grunert Arch. 38 (1862) 259-. 

 Bachmann, P. Z. Mth. Ps. 16 (1871) 181-. 

 Siacci, F. Em. At. E. Ac. 25 (1872) 339-. 

 Bachmann, P. Crelle J. Mth. 76 (1873) 331-. 

 Korkine, A.,<& Zolotareff, G. Mth. A. 6 (1873) 



366-. 



Frobenius, G. C. E. 85 (1877) 131-. 

 Jordan, C. Par. EC. Pol. J. Cah. 51 (1882) 1-. 

 Minkowski, H. Acta Mth. 7 (1885) 201-. 

 Algorithm for treatment. Hermes, J. [1881] 



Arch. Mth. Ps. 68 (1882) 432-. 

 Application to complex variables. Preobra- 



schensky, P. W. Fschr. Mth. (1898) 176. 

 Composition. Bazin, . Liouv. J. Mth. 16 



(1851) 161-. 

 . Arndt, F. Crelle J. 56 (1859) 64-. 



Decomposition of numbers into sums 

 of squares. 



Malfatti, G. F. Mod. S. It. Mm. 12 (1805) 



296-. 

 Plana, G. [1859] Tor. Mm. Ac. 20 (1863) 113-. 



209 



