2860 



Wilson's theorem, generalisation. Lognon, 



N. A. Mth. 15 (1896) 503. 

 , Lagrange's proof. Lista, A. Cadiz 



Period. M. Ci. 1 (1848) 63-. 

 , point arising in. Liouville, J. Liouv. 



J. Mth. 5 (1860) 127-, 267-. 



2860. Forms of higher degree 

 which cannot be considered as 

 products of linear factors. (See 

 also 2060, 2070.) 



Algebraic forms with arithmetical connexions. 



Cesdro, E. Bm. E. Ac. Line. Ed. 2 (1886) 



(San. 2) 56-. 

 Biquadratics, pairs of sums of two. Euler, L. 



St Pet. Ac. Sc. Mm. 11 (1830) 49-. 

 Congruences, theorems. Libri, G. Crelle J. 



9 (1832) 54-, 169-, 261-. 

 , . Lebesgue, V. A. Liouv. J. Mth. 2 



(1837) 253- ; 3 (1838) 113- ; 4 (1839) 9-. 

 Cube = sum of three cubes, Euler's solution. 



Binet, J. P. M. C. E. 12 (1841) 248-. 

 Cubic classes belonging to determining quad- 

 ratic form, number. Arndt, F. Grunert 



Arch. 19 (1852) 408-. 



forms. Eisenstein, G. Crelle J. 27 (1844) 75-. 



and quartic forms, reduction to squares. 

 Euler, L. [1780] St Pet. Ac. Sc. Mm. 11 

 (1830) 69-. 



Decomposition of number into four / positive 



cubes, theorem of Euler. Lucas, E. N. A. 



Mth. 19 (1880) 89-. 

 its maximal nth powers. Lemoine, 



E. C. B. 95 (1882) 719-. 

 Diophantine equations of class zero. Hilbert, 



D., & Hurwitz, A. Acta Mth. 14 (1890-91 



217-. 



problem, geometrical solution. Burhenne, 

 H. Grunert Arch. 20 (1853) 466-. 



triangles, problem of Fermat. Tannery, P. 

 [1885] Par. S. Mth. Bll. 14 (1886) 41-. 



Equations between two variables, integral solu- 

 tions. Eunge, C. Crelle J. Mth. 100 (1887) 

 425-. 



. x 5 + y s = az 5 . Lebesgue, V. A. Liouv. J. 

 Mth. 8 (1843) 49-. 



. x 3 + y 3 + Az 3 = Mxyz> Sylvester, J. J. Ph. 

 Mg. 31 (1847) 467-. 



Higher Irresolvable Forms 2860 



Equations, x 3 + y 3 + z 3 + u 3 = 0. Grassmann, H . 



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

 x*+y*=z 3 + u s . Hermite,C. N. A. Mth. 



11 (1872) 5-. 

 . x 3 =i/ 2 + 17. Gerono, C. C. N. A. Mth. 16 



(1877) 325-. 



. ax* + by*=cz 2 . Desboves, A. C. E. 87 



(1878) 522-, 598-, 925. 



. x s a = 2/ 2 . Jonquie.res,E. de. N. A. Mth. 

 17 (1878) 374-, 514-. 



- - . . Lucas, E. As. 



, -. 



- ( 

 \ P 



Fr. C. B. (1878) 164-. 



. X 3 +Y 3 =AZ 3 . Lucas, E. N. A. Mth. 17 



(1878) 425-. 



Desboves, A. C. B. 88 (1879) 638-. 



. Ax* + By*=Cz*. Lucas, E. N. A. Mth. 18 

 (1879) 67-. 



m 



Desboves, A. N. A. 

 Mth. 18 (1879) 265-, 398-, 433-, 481-. 



. 7.r 4 -5i/*=2 Z 2 . Pepin,T. Liouv. J. Mth. 

 5 (1879) 405-. 



_. U n V n = S n +W n , solution in integers, 

 real or complex. Desboves, A. As. Fr. C. 

 B. 9 (1880) 239-. 



. x 3 + y s =Az 3 . Lucas, E. N. A. Mth. 19 

 (1880) 206-. 



. ax* + by* = z- 2 . Pepin, T. C. E. 91 (1880) 

 100- ; 94 (1882) 122-. 



. x n + y n + z n =U n . Schier,0. [1880] Wien 

 Ak. Sb. 82 (1881) (Ab. 2) 883-. 



. x* + y 3 = Az 3 . Pepin, T. Em. N. Line. At. 

 34 (1881) 73-. 



. ax t + by t =cz*. Pepin, T. [1882] Em. N. 

 Line. At. 36 (1883) 34-. 



. aX 4 -6Y 4 = 2Z 2 . Desboves, A. As. Fr. C. 

 B. (1887) (Pt. 1) 175. 



. aX* + bY i = cZ 2 . Desboves, A. C. B. 104 

 (1887) 846-, 1602-. 



. aX* + bY*=cZ*, andaX 4 + bY* + dX 2 Y*= cZ*. 

 Desboves, A. C. B. 104 (1887) 1832-. 



. U* + F 4 = S 4 + W*. Fauquembergue, E. 

 Mathesis 9 (1889) 241-. 



. z 2 + cF 2 = 2. Pepin, T. Em. N. Line. 

 Mm. 8 (1892) 41-. 



. x t >+y 5 = 2 m z*. Levdnen, S. Helsingf. 

 Ofv. 35 (1893) 69-. 



. X* + 35Y* = Z*. Pepin, . Liouv. J. 

 Mth. 1 (1895) 351--. 



V. A. 



x* 2 i/ 4 and 2*z* = x* y 4 . Lebesgue, ,.. ax + by* = cz*. Maillet, E. As. Fr. C. 



Liouv. J. Mth. 18 (1853) 73-. 



. ax + bky = z(x* + ky*). Oltramare,G. Crelle 

 J. 49 (1855) 142-. 



. x 3 + y 3 =z 2 , solution in relative primes. 

 Hoppe, R. Schlomilch Z. 4 (1859) 304-. 



. a; 3 + y 3 = x - y , solution in rational numbers . 

 Hoppe, R. Schlomilch Z. 4 (1859) 359-. 



. x 3 + y 3 + z 3 =v 3 . Bunlakovskij, V. [1864] 

 StPet. Ac. Sc.Mm. (Rs.) 6 (*1865) 142-. 



. x 3 + y 3 + z 3 = w 2 , solution by toroid. Catalan, 

 . E. C. Brux. Ac. Bll. 22 (1866) 29-. 



. x 3 + y 3 + z 3 =u 3 . Richaud,C. Em. At. N. 

 Line. 19 (1866) 183-. 



Rickaud, C. Em. At'. N. Line. 20 (1867) 91-.' 



B. (1897) (Pt. 2) 156-. 

 . a; 4 -8.rV + 8t/ 4 = 2 2 . Pepin, T. Bm. N. 



Line. Mm. 14 (1898) 71-. 

 . x 4 + 4^V+(2/z-l)V=2 2 > where 4ft -1 



and 2/i - 1 are primes. Pietrocola, C. G. 



Mt. 36 (1898) 77-. 

 . * A + w*=cA Maillet, E. C. E. 129 



198-. ' 



FermaVs theorem on x n + y n =z n . 



Barlow, P. Nicholson J. 27 (1810) 193-. 

 Legendre, A. M. Par. Mm. Ac. Sc. 6 (1823) 



Lam6, G. [1839] C. E. 9 (1839) 45-; Par. 

 Mm. Sav. Etr. 8 (1843) 421-. 



218 



