1610 



Rational polynomials; divisibility; reducibility 



1610 



Binomials, cube-roots. Homer, W. G. Thom- 

 son A. Ph. 8 (1816) 279-, 388-. 



, cubic, x*y 3 . Lame, G. C. E. 61 (1865) 

 921-, 961-. 



Common divisors, finding. Buys-Ballot,C.H. D. 

 Amst. Vs. Ak. 13 (1862) 430-. 



Condition that/=^0 + J5\t-, where/, A, B, <j>, $ 

 are all rational integral polynomials in two 

 variables. Halphen, G. H. Par. S. Mth. 

 Bll. 5 (1877) 160-. 



Divisibility of (x + y) n + ( - x) n + ( - y) n , Cauchy's 

 theorem. Muir, T. [1878] Mess. Mth. 8 

 (1879 119-. 



, . Lucas, E. As. Fr. C. E. 



(1888) (Ft. 2) 29-. 



Division, abbreviated algebraic. Reuschle, C. 

 Z. Mth. Ps. 41 (1896) 93-. 



, algebraic, applied to homogeneous poly- 

 nomials. Andoyer, H. Liouv. J. Mth. 1 

 (1895) 61-. 



, , and new theorem of analysis. Le Cointe, 

 L. A. N. A. Mth. 1 (1842) 409-. 



of integral polynomials, application to in- 

 tegration. Jamet, V. Mars. Fac. Sc. A. 8 

 (1898) 151-. 



polynomial by another. Rubini, R. G. 



Mt. 4 (1866) 38-. 

 Divisors, algebraic theorem, with application 



to curves. Pasch, M. Crelle J. Mth. 89 



(1880) 252-. 

 , commensurable, 2nd degree. Transon, A. 



(Prof.). N. A. Mth. 6 (1847) 305-. 

 _, , . Prouhet, E. N. A. Mth. 18 



(1859) 257-. 

 given degree of a polynomial. Maleyx, L. 



N. A. Mth. 14 (1875) 97-. 



polynomials with whole numbers for 

 coefficients. Perott, J. Par. S. Mth. Bll. 

 10 (1882) 250-. 



, rational. Durville, . N. A. Mth. 4 (1845) 



439-. 

 , , 2nd degree. Durville, . N. A. Mth. 



4 (1845) 339-. 



of rational polynomials. Bouniakowsky , V. 

 [1854] St Pet. Ac. Sc. Mm. 8 (1857) 305-. 



Equations with integral coefficients. Cauchy, 



A. L. C. E. 24 (1847) 407-. 

 Expansion of (l+x + x 2 + ...&c.)". Euler, L. 



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



47-. 

 (l + x + x*) n . Euler, L. [1778] St Pet. 



Ac. Sc. N. Acta 14 (1805) 75-. 

 (x + y) n + (-x) n + (-y) n . Muir, T. QJ. 



Mth. 16 (1879) 9-. 

 Factorials, class/ Gregory, D. F. Camb. Mth. 



J. 3 (1843) 89-. 



Vandermonde's. Anon, (vi 158) Bb. It. 

 (1830) 407-. 



Factorization. Butters, J. W. Edinb. Mth. 



S. P. 12 (1894) 31-; 16 (1898) 78-. 

 Factors of integral functions of nth degree. 



Am Ende, . Grunert Arch. 30 (1858) 



442-. 



ax* + bxy +...+/. Grunert, J. A. 

 Grunert Arch. 39 (1862) 98-. 



(x + y) n - x n - y n , Cauchy's theorem. 



Glaisher, J. W. L. QJ. Mth. 15 (1878) 365- ; 

 16 (1879) 89-. 



Figurate series. Smyth, B. B. Kan. Ac. Sc. 



T. 14 (1896) 29-. 

 Formation-law of coefficients in quotient of two 



power series. Jeiek, 0. Prag Sb. (1884) 



(Mth. Nt.) 127-. 

 Formula giving x m + y m as function of (x + y) 



and xy. Desboves, A. N. A. Mth. 14 (1875) 



385-. 

 H. C. D. Bouverat, . N. A. Mth. 3 (1844) 



329-. 

 --- . Cirodde, P. L. N. A. Mth. 4 (1845) 



497-. 

 --- of 2 functions of one variable . Trudi , N. 



Nap. Ed. 1 (1862) 153-. 

 ----- integral functions. Netto, E. 



[1889] Hamb. Mth. Gs. Mt. 2 (1890) (Fest- 



schr. Tl. 2) 36-. 

 ---- polynomials. Pomey, E. 



N. A. Mth. 7 (1888) 66-, 407-. 

 --- and L. C. M. Barrieu, P. (xn) 



Mathesis 3 (1883) 217-. 

 --- of 2 polynomials. Craufurd, A.Q. G. 



Camb. Mth. J. 4 (1845) 9-. 



, remainder in the pro- 

 cess. Faa de Bruno, F. C. E. 42 (1856) 

 407-. 



polynomials, determination by 

 determinants. Zeuthen, H. G. (xn) Ts. 

 Mth. 5 (1881) 45-, 109-. 



---- 2 rational integral functions of x, 



method. Falk, M. [1878] Ups. S. Sc. N. 



Acta 10 (1879) (No. 11) 5 pp. 

 Homogeneous functions, property. Gukovskij, 



A. N. Es. S. Nt. Mm. (Mth.) 11 (1890) 



145-. 

 Identities, algebraic class. Glaisher, J. W. L. 



[1878] Mess. Mth. 8 (1879) 53-. 



, , relating to sums of squares. Catalan, 

 E. C. Liege S. Sc. Mm. 13 (1886) 33-, 

 399. 



, connected with (a + b) n - a* - b n . Sadun, E. 

 Ev. Mt. 4 (1894) 189- ; 5 (1895) 19-. 



developed from- = - + ^^.-. Tait,P.G. 



p q q p 



[1877] Edinb. E. S. P. 9 (1878) 416-. 

 Identity, algebraic, on differences of 4 letters. 

 Glaisher, J. W. L. [1878] Mess. Mth. 8 

 (1879) 45-. 



, , reciprocals of cyclic differences. 

 Saint-Germain, de. Caen Ac. Mm. (1892) 

 (Pt. 1) 15-. 



of polynomials, principle. Roy, A. Mathe- 

 matician 3 (1850) 1-. 



-- Waring's, an. Virieu, J. de. N. A. Mth. 

 1 (1862) 45-. 



, Waring's analytical proof. Serret, P. N. 

 A. Mth. 7 (1848) 199-. 



. Ifa + 6 + c=0, 



(b-c c-a a-b\ 

 - + r- + - I 

 a b c J 



b 



Glaisher, J. W. L. [1880] Mess. Mth. 10 

 (1881) 54-. 



Irreducible factors of x n -l. Kronecker, L. 

 Liouv. J. Mth. 19 (1854) 177-. 



78 



