2810 Divisibility 



Divisibility; linear congruences 2810 



by number 7. Brooks, E. Des Moines Anal. 



2 (1875) 129-. 

 . Evans, A. Des Moines Anal. 10 



(1883) 134-. 

 , and conversion of fractions. Reyer, 



A. P. Grunert Arch. 25 (1855) 176-. 



, criteria. Heilinann, J. Ev. Sc. 38 

 (1886) 187. 



9, criterion, generalisation. Wilbra- 

 Jiam, H. Camb. and Dubl. Mth. J. 6 (1851) 

 32-. 



13. Breton, P. Ev. Sc. 38 (1886) 



444-. 

 . Sclwbbens, . Ev. Sc. i 



445. 

 19. Badoureau, A. N. A. Mth. 18 (1879) 



35-. 



numbers 7, 11, 13, tests. Grunert, J. A. 

 Arch. Mth. Ps. 42 (1864) 478-. 



and 13 especially. Pinaud, A. Toul. 



Mm. Ac. 1 (1844) 341-, 347-. 

 , tests. Lindman, C. F. Grunert 



Arch. 26 (1856) 467-. 

 of numbers of form 2 2 " + l, new case (Pervou- 



chine). Bouniakowsky, V. St Pe"t. Ac. Sc. 



Bll. 24 (1878) 559 ; 25 (1879) 63-. 



one given number by another. Schlegel, 

 S. F. V. Z. Mth. Ps. 21 (1876) 365-. 



product of factorials by another, con- 

 ditions. Landau, E. N. A. Mth. 19 (1900) 

 344-. 



by power of 2, theorem. Fregier, . Ger- 

 gonne A. Mth. 9 (1818-19) 285-. 



prime numbers. Sensenig, D. M. Des 

 Moines Anal. 3 (1876) 25-. 



a prime to 10. Dietz, , & Vincenot, . 

 Metz Mm. Ac. 33 (1851-52) 37-. 



problem. Elefanti, F. E. S. P. 10 (1859-60) 



208-. 

 of product, distribution of primes. Catalan, 



E. C. Liege S. Sc. Mm. 12 (1885) No. 2, 



20-, 119-. 

 question; Polignac, C. (Prince) de. C. E. 96 



(1883) 485-. 



simple properties. Elliott, E. B. Mess. Mth. 



27 (1898) 12-. 



of sum of products of first n numbers taken 

 r together. Glaisher, J. W. L. Mess. Mth. 



28 (1899) 184-. 



theorem. Crelle, A. L. Crelle J. 5 (1830) 

 296 ; Gergonne A. Mth. 20 (1829-30) 349-. 

 . R., O. , N. A. Mth. 4 (1845) 81-. 

 . Bauer, M. Mth. Nt. B. Ung. 15 (1899) 



of Euler, correction. Chevillier, I. N. A. 

 Mth. 14 (1855) 433-; 15 (1856) 260-. 



theorems. Catalan, E. Brux. Ac. Bll. 7 



(1884) 448-. 



. Allardice, R. E. Edinb. Mth. S. P. 8 

 (1890) 16-. 



oi n(r + i) by n!, proof. Greatheed, S. S. 

 (n Adds.) Camb. Mth. J. 1 (1839) 102-, 



n!, theorem. Gomes Teixeira, F. Arch. 

 Mth. Ps. 2 (1885) 265-. 



Division of a number by 9 or 11. Dodgson, 



C. L. Nt. 56 (1897) 565-. 

 numbers, general law. Bugaev, N. Eec. 



Mth. (Moscou) 12 (1885) 283-j Fschr. Mth. 



(1885) 145-. 



by a prime, theorem. Mantel, W. N. Arch. 

 Wisk. 4 (*1878) 57-. 



, . Oskamp, G. A. N. Arch. 



Wisk. 4 (*1878) 83-. 

 , theorem. Lejeune-Dirichlet, G, Berl. B. 



(1851) 20-. 

 , on remainders (Lejeune-Dirichlet). Ter- 



quem, 0. N. A. Mth. 13 (1854) 396-. 

 Divisors in case of two arbitrary functions, 



theorem. Bugaev, N. V. [1867] (xn) Eec. 



Mth. (Moscou) 3 (1868) (Pt. 1) 69-. 

 , construction of tables. Davis, W. B. L. 



Mth. S. P. 4 (1873) 416-. 



of first n numbers, relations. Glaisher, 

 J. W. L. L. Mth. S. P. 22 (1891) 359-. 



an integer. Lionnet, E. N. A. Mth. 7 



(1868) 68-. 

 , which exceed an assigned limit. 



Gegenbauer, L. Wien Ak. Sb. 98 (1890) 



(Ab. 2a) 28-. 

 integers. Gegenbauer, L. Wien Ak. Sb. 



91 (1885) (Ab. 2) 600-. 

 . Eaorov, D. T. [1891] Eec. Mth. 



"loscou) 16 (1893) 236-; Fschr. Mth. (1892) 



(Me 



iss 



number. Crelle, A. L. Berl. Ab. (1832) 



33-. 

 . Hain, E. Arch. Mth. Ps. 55 (1873) 



290-. 

 , formula of Euler, proof. Lebesgue, 



V. A. N. A. Mth. 12 (1853) 232-. 

 , method of finding. Canterzani, S. 



Bologna Mm. I. It. 2 (pte. 2) (1810) 445-. 

 , ^ functions. Gegenbauer, L. Wien 



Ak. Sb. 93 (1886) (Ab. 2) 447-. 

 , . Lerch, M. Prag Sb. (1887) 



(Mth.-Nt.) 683-; (1894) (Mth.-Nt.) No. 11, 



11 pp., No. 32, 20 pp. 

 , theorems. Glaisher, J. W. L. [1875] 



Mess. Mth. 5 (1876) 52. 

 , . Gegenbauer, L. Wien Ak. Sb. 



91 (1885) (Ab. 2) 1194-. 

 , . Cesdro, E. G. Teix. J. Sc. 



7 (1886) 3-. 

 , . Lerch, M. Bll. Sc. Mth. 12 



(1888) 100- ; Casopis 21 (1892) 90-, 185- ; 



Fschr. Mth. (1892) 186-. 

 , . Bugaev, N. V. [1893-1898] 



Eec. Mth. (Moscou) 17 (1895) 720- ; 20 



(1899) 549-; Fschr. Mth. (1895) 218- ; (1899) 



194. 

 , , two. Nachtikal, F. Casopis 



25 (1896) 344-; Fschr. Mth. (1896) 139. 

 numbers, graphic representation. Saint- 



Loup, L. C. E. 107 (1888) 24-; Par. EC. 



Norm. A. 7 (1890) 89-. 

 and products of factors. Roberts, S. 



QJ. Mth. 20 (1885) 370-. 

 prime, theorem concerning remainders. 



Gauss, C. F. Gott. Cm. 16 (1804-08) 69-. 

 , reduction of systems. Hensel, K. Crelle 



J. Mth. 118 (1897) 234-; 119 (1898) 114-. 



194 



