2810 



Divisibility; linear congruences 



2810 



Divisors of series of natural numbers. Busche, 

 E. [1896] Hamb. Mth. Gs. Mt. 3 (1900) 

 234-. 



2w, Liouville's theorem. Mathews, 

 G. B. [1893] L. Mth. S. P. 25 (1894) 

 85-. 



E (<px) applied to determine integral part of 



quotient of two polynomials. Bugaev, N. V. 



[1897] Rec. Mth. (Moscou) 20 (1899) 247-; 



Fschr. Mth. (1898) 70. 

 Equation (<f>) m (<) n = (<p) mn. Hammond, J. 



Mess. Mth. 24 (1895) 17-. 

 Factorial N, divisors. Weitt, M. C. E. 93 



(1881) 1066-. 

 Factorials, property. Lerch, M. Prag Sb. 



(1898) (Mth.-Nt.) No. 2, 4 pp. 

 Factorisation. Kausler, C. F. [1801] St Pet. 



Ac. Sc. N. Acta 14 (1805) 268-. 

 . Bouniakowsky, V. [1839] St Pet. Ac. Sc. 



Mm. 4 (1841) 447-. 

 . Collins, E. [1839] St Pe"t. Ac. Sc. Bll. 6 



(1840) 84-. 

 . Catalan, E. C. As. Fr. C. E. 9 (1880) 



228-. 



. Busk, C. J. Nt. 39 (1889) 413-. 

 . Hudson, W. H. H. Nt. 39 (1889) 510-. 

 . Cunningham, (Lt.-Col.) A. Mess. Mth. 



20 (1891) 37-. 

 . Thaarup, F. N. Ts. Mth. 2 (A) (1891) 



49-; Fschr. Mth. (1891) 190. 

 . Selivanov, D. T. Eec. Mth. (Moscou) 15 



(1891) 789-; 16 (1893) 469-; Fschr. Mth. 



(1891) 191- ; (1892) 164. 

 . Lawrence, F. W. Mess. Mth. 24 (1895) 



100- ; QJ. Mth. 28 (1896) 285-. 

 . Biddle, D. Mess. Mth. 28 (1899) 116-, 



192. 

 . Seliwanow, D. F. Fschr. Mth. (1899) 



172-. 



of certain product (of integers). Gmeiner, 

 J. A. Mh. Mth. Ps. 1 (1890) 159-. 



large numbers. Lucas, E. C. E. 83 

 (1876) 1286-. 



, method. Winter, G. K. Madras J. (1886- 



87) 13-. 

 , problem. Eados, 'G. Mth. Termt. Ets. 



3 (1885) 178-. 

 , Tesanek's method. Studnicka, F. J. 



Casopis 14 (1885) 120- ; Fschr. Mth. (1885) 



125. 

 Factorisations of an integer in two factors of 



prescribed form, mean number. Gegenbauer, 



L. Wien Ak. Sb. 93 (1886) (Ab. 2) 90-. 

 Factors of certain numbers. Workman, W. P. 



Mess. Mth. 24 (1895) 67. 

 composite numbers. Hill, C. J. D. Crelle 



J. 11 (1834) 251-. 

 Mobius. Koch, H. von. Stockh. Ofv. 



(1900) 659-. 



numbers. Cunningliam, (Lt.-Col,') A. 

 Nt. 39 (1889) 559-. 



. Speckmann, G. Arch. Mth. Ps. 12 



(1894) 435-. 



, general rule for. Zeipel, E. V. von. 



Stockh. Ofv. 18 (1861) 425-. 

 , plan for table. Crelle, A. L. Crelle 



J. 51 (1856) 61-. 



Factors, table, geometric properties. Mobius, 



A. F. Crelle J. 22 (1841) 276-. 

 Faculties. Mathieu, E. N. A. Mth. 17 (1858) 



235-. 

 . Lebesgue, V. A. N. A. Mth. 19 (1860) 



112-, 135-. 



. Guibert,A. N. A. Mth. 1 (1862) 102-. 

 , problem. Berton, . N. A. Mth. 18 (1859) 



191. 

 , . Hill, G. W. Des Moines Anal. 1 (1874) 



27-. 

 Generalised Euler function, geometrical proof 



of theorems. Daublebsky von Sterneck, E. 



Mh. Mth. Ps. 5 (1894) 255-. 

 Greatest common divisor. Gegenbauer, L. Wien 



Ak. Sb. 97 (1889) (Ab. 2a) 420-. 

 of all numbers represented by integral 



function of n variables. Hensel, K. Crelle 



J. Mth. 116 (1896) 350-. 



, asymptotic laws. Gegenbauer, L. 

 Wien Ak. Sb. 92 (1886) (Ab. 2) 1290-. 



divisors. Gegenbauer, L. Wien Ak. Sb. 

 94 (1887) (Ab. 2) 714-. 



prime divisor of ?i 2 +l, theorem. Markqff, 

 A. C. E. 120 (1895) 1032-. 



square divisor. Cesdro, E. A. Mt. 13 (1885) 

 251-. 



Harmonic series, divisibility. Birkenmajer, L. 

 Prace Mt.-Fiz. 7 (1896) 12-; Fschr. Mth. 



(1896) 141. 



Identity, Clausen's, arithmetical proof. 

 Glaisher, J. W. L. [1875] Mess. Mth. 5 

 (1876) 83. 



Integers divisible by sum of their divisors. 

 Minin, A. P. [1893] Eec. Mth. (Moscou) 17 

 (1895) 240- ; Fschr. Mth. (1893-94) 277. 



Kronecker's principle of equivalence. Busche, 

 E. [1891] Hamb. Mth. Gs. Mt. 3 (1900) 3-. 



Linear congruence, several unknowns. Le- 

 besgue, V. A. Liouv. J. Mth. 4 (1859) 366. 



congruences, formulae for resolution. 

 Zehfuss, G. Grunert Arch. 32 (1859) 422-. 



, homogeneous. Steinitz, E. [1896] D. 



Mth. Vr. Jbr. 5 (1901) (Heft 1) 87. 

 , modular system. Kronecker, L. Crelle 



J. Mth. 99 (1886) 329-. 

 1 system. Burnside, W. Mess. Mth. 24 



(1895) 51-. 

 , , solution. Studnicka, F. J. Prag 



Sb. (1875) 114-. 

 , systems. Smith, H. J. S. L. Mth. S. P. 



4 (1871-73) 241-. 

 , transformation of moduli. Bouniakowsky, 



V. N. A. Mth. 18 (1859) 168-. 



forms and congruence groups, composition. 

 Stouff, X. C. E. 119 (1894) 993-. 



-with integral coefficients. Frobenius, G. 



[1878-79] Crelle J. Mth. 86 (1879) 146- ; 



88 (1880) 96-. 

 variables. Hurwitz, A. Gott. Nr. 



(1897) 139-. 



representing primes. Vahlen, T. Konigsb. 



Schr. 38 (1897) [47]. 

 " Manifoldness " of a number (number of 



distinct prime divisors). Sylvester, J. J. 



Nt. 37 (1888) 152-, 179. 

 Moduli, 11, 9, 13, 101, tests. Anton, H. Arch. 



Mth. Ps. 49 (1869) 241-. 



195 



