2815 Indeterminate equations 



solution. Ayza, E. Fschr. Mth. (1897) 168. 

 , forms. Weihrauch, K. Z. Mth. Ps. 19 



(1874) 53-. 

 systems. Smith, H. J. S. B. A. Rp. (1860) 



(pt. 2) 6; Phil. Trans. (1861) 293-. 

 . Ovidio, E. d'. Tor. Ac. Sc. At. 12 (1876) 



334-. 

 2 or more variables, solution by continued 



fractions. Pleskot, A. Casopis 22 (1893) 71- ; 



Fschr. Mth. (1893-94) 278. 

 4 variables, solutions, number. Weihrauch, K. 



Z. Mth. Ps. 22 (1877) 234-. 

 n variables. Sylvester, J. J. Ph. Mg. 16 (1858) 



369-. 



2nd order. 



Minding, E. F. A. Crelle J. 7 (1831) 140-. 

 Arndt, F. Grunert Arch. 12 (1849) 211-. 

 Gopel, A. Crelle J. 45 (1853) 1-. 

 Realis, S. N. A. Mth. 3 (1884) 305-, 448. 

 Desboves, A. N. A. Mth. 5 (1886) 226-. 

 Marcolongo, E. G. Mt. 25 (1887) 161- ; 26 



(1888) 65-. 

 Jonquieres, de. C. R. 126 (1898) 863-, 990, 



991. 

 Euler's formula. Chasles, M. Liouv. J. Mth. 



2 (1837) 37-. 

 and fourth. Pepin, T. Em. N. Line. At. 32 



(1879) 79-. 



Lagrange's and Gauss's methods. Jonquieres, 



de. C. R. 127 (1898) 694-. 

 solution. Kunerth, A. Wien Ak. Sb. 75 (1877) 



(Ab. 2) 7-. 



by continued fraction, criteria. Kunerth, A. 

 [1880] Wien. Ak. Sb. 82 (1881) (Ab. 2) 

 342-. 



in rational numbers. Kunerth, A. [18781 

 Wien Ak. Sb. 78 (1879) (Ab. 2) 327-. 



3rd order. 



Realis, S. N. A. Mth. 17 (1878) 454-. 

 Jonquieres, E. de. Em. N. Line. At. 37 (1884) 



183-. 

 or higher. Desboves, A. C. R. 87 (1878) 159-, 



321-. 

 impossibility. Lucas, E. Par. S. Mth. Bll. 8 



(1880) 173-. 



and problem of Sylvester's. Lucas, E. N. A. 



Mth. 17 (1878) 507- ; Am. J. Mth. 2 (1879) 



178. 

 reduction to 2nd order. Le Besgue, V.A. C. E. 



64 (1867) 1267-. 



4th order. 



Pepin, T. Em. N. Line. At. 31 (1878) 397- ; 



Em. N. Line. Mm. 4 (1888) 227-; 9 (1893) 



(Pt. 1) 247-; 11 (1895) 223-. 

 with 4 variables, solution. Eisenstein, G. 



Crelle J. 27 (1844) 75-. 



5th order. 



impossibility of some equations. Lejeune- 

 Dirichlet, G. Crelle J. 3 (1828) 354-. 



Indeterminate equations 2815 



ab (ma? + nV*)=cd (me 2 -Mid 2 ). Eider, L. [1778] 



St Pet. Ac. Sc. N. Acta 13 (1802) 45-. 

 = 1 + bx + cy + dx* + cxy + fy* + gx-y + hxy* 



+ ix z y z . Euler, L. St Pet. Ac. Sc. Mm. 11 



(1830) 58-. 

 4 (x* - 1) = (x - 1) (F 2 nZ 2 ) . Legendre, A . M. 



[1830] Par. Mm. Ac. Sc. 11 (1832) 81-. 

 4 (XP - 1) = ( x - 1) (i/ 2 pz 2 ). Germain, (Mile.) S. 



Crelle J. 7 (1831) 201-. 

 2 2 "-?/=2.r. Liouville,J. Liouv. J. Mth. 5 



(1840) 360. 

 x m -y*=l. Catalan, E. C. Crelle J. 27 (1844) 



192. 

 j/ = cos7r.r, solution in rational numbers. 



Schulten, N. G. af (fil.) [1844] Helsingf. 



Acta 2 (1847) 617-. 

 ax + by + cz = Q. Cauchy, A. L. Grunert Arch. 



7 (1846) 305-. 

 Ax 3 + By 3 +Cz 3 = Dxyz. Sylvester, J. J. Ph. 



Mg. 31 (1847) 189- , 293-. 

 ax + by = c. Dieu, T. N. A. Mth. 9 (1850) 67-. 

 ax (a + b) y = m. Grebe, E. W. Grunert Arch. 



14 (1850) 333-. 

 a a x 2 = a,Xj + 1, smallest integers satisfying. 



Crelle, A. L. Berl. B. (1850) 141- ; Crelle J. 



42 (1852) 299-. 



x m =y'^+l, impossibility of solution in inte- 

 gers. Lebesgue, V. A. N. A. Mth. 9 (1850) 



178-. 

 a x - bv= 1, a and b being primes. Gerono, G. C. 



N. A. Mth. 16 (1857) 394-. 

 ax + by + cz + , etc. = n, number of solutions in 



positive integers. Hermite, C. QJ. Mth. 1 



(1857) 370-. 

 aj + 2a 2 + 3a 3 +...+na n =n. Fergola, E. Nap. 



Ed. 2 (1863) 262-. 

 ns [s 2 + (n- - 1) r 2 ] = 8y 3 . Le Besgue, V. A . (vm) 



A. Mt. 5 (1863) 328. 



_ = _. Genocchi,A. (vn) A. Mt. 5 (1863) 329-. 

 (x + h) n -x n = z n , impossibility. Gaudin, . 



C. E. 59 (1864) 1036-. 

 Ax + By = S. Clasen, B. I. Par. EC. Norm. A. 



4 (1867) 347-. 

 4 (xf>-l) = (x-l) (y-pz"*). Staudt, G. K. C. 



von. Crelle J. 67 (1867) 205-. 

 S<Vr r =/. M . Jacobi, C. G. J. Crelle J. 69 



(1868) 1-. 

 x m = y n + l. Gerono, G.C. N. A. Mth. 9 (1870) 



469- ; 10 (1871) 204-. 

 ax + by + cz=m. Gambardella, F. G. Mt. 9 



(1871) 262-. 



ax + by = c, solution in integers, graphic repre- 

 sentation. Polignac, C. (Prince) de. [1877] 



Par. S. Mth. Bll. 6 (1878) 158-. 

 Z = M, x + l = 2v 2 , 2x + l = 3iv*. Gerono, C. C. 



N. A. Mth. 17 (1878) 381-. 

 ar=4 a + l, * 2 = z 2 +(z + l) 2 . Gerono, C. C. N. 



A. Mth. 17 (1878) 521-. 

 Ax + B = 4>(Cx + D). Serdoblnskii, V. E. [1878] 



(xn) Eec. Mth. (Moscou) 9 (1878-81) (Pt. 1) 

 557 . 



'iTx^r; *2;"iX f = n. Sadun, E. A. Mt. 15 



t " 1 (1887-88) t 209-. 



= t/ 3 , posthumous problem of Leibnitz. 

 Studnicka, F. J. Casopis 18 (1889) 97-; 

 Fschr. Mth. (1889) 30-. 



203 



