2810 



Divisibility; linear congruences 



Non-equivalent rectangular arrays, enumera- 

 tion. Ltmdsberg, G. Crelle J. Mth. Ill 

 (1893) 87-. 



Number of congruent divisors of a number. 

 Traub, C. Grunert Arch. 37 (1861) 277-. 



divisors of all numbers from 1 to n. 

 Busche, E. [1894] Hamb. Mth. Gs. Mt. 

 3 (1900) 167-. 



, application of geometry to theory 

 of numbers. Schroder, J. [1894] Hamb. 

 Mth. Gs. Mt. 3 (1900) 177-. 



, generalisation of theorem. Schroder, 



J. [1895] Hamb. Mth. Gs. Mt. 3 (1900) 



219-. 

 of given number, etc. Ettingshausen, 



A. von. Baumgartner Z. 5 (1829) 287-. 

 integer. Stieltjes, T .J. (jun.) 



C. E. 96 (1883) 764-. 

 , MSS. of Michael Stifel. Hoppe, E. 



Hamb. Mth. Gs. Mt. 3 (1900) 411-. 

 -of odd number having form 4ft 1, 



8fcl, 87i3. Andreevskil, M. A. [1869] 



(xn) Eec. Mth. (Moscou) 6 (1872-73) (Pt. 1) 



< - a, theorem. Gomes Teixeira, 

 P. G. Teix. J. Sc. 3 (1881) 105-. 

 integers prime to m and < m/k. Laguerre, 



E. (x) Par. S. Mth. Bll. 1 (1873) 77-. 

 numbers in a set not divisible by a prime. 



Lipschitz, R. O. S. C. E. 96 (1883) 327-. 

 Numbers divisible by 7 and by 2, 3, 4, 5, 6, 



with remainder 1. Wiedemann, E. Erlang. 



Ps. Md. S. Sb. 24 (1892) 83. 

 , geometrical representation according to 



modulus p. Laisant, C. A. As. Fr. C. E. 



(1887) (Pt. 2) 218-. 



not divisible by squares, series of. Lipschitz, 

 R. 0. S. C. E. 89 (1879) 948-, 985-. 



prime to given number. Rocquigny, F. [G.] 

 de. Les Mondes 52 (1880) 516-. 



one another. Guilmin, A. N. A. 

 Mth. 10 (1851) 23-. 



. Schemmel, V. [1868] Crelle 



J. 70 (1869) 191-. 

 . Goldschmidt, L. Z. Mth. 



Ps. 39 (1894) 203-. 



given number and less than another. 



Rocquigny, F. [G.] de. Les Mondes 50 (1879) 



604-. 

 . Minine, A. 



Les Mondes 51 (1880) 333-; 53 (1880) 526-. 

 . NazHnov, P. S. 



[1881] (xn) Eec. Mth. (Moscou) 11 (1883- 



84) 603-. 

 , various theorems. Dienger, J. Grunert 



Arch. 12 (1849) 425-; 16 (1851) 120-. 

 Numerical divisors of polynomials. Borel, E. 



Bll. Sc. Mth. 24 (1900) 75-. 



factors. Birch, (Rev.) J. G. Mess. Mth. 

 22 (1893) 52-. 



of a - 1. Bickmore, C. E. Mess. Mth. 



25 (1896) 1-; 26 (1897) 1-. 

 Periodic division series, properties. Poselger, 



F. T. Berl. Ab. (1827) 21-. 



Prime factors, determination. Stouff, . N. 



A. Mth. 10 (1871) 104-. 

 , , Gauss's tables. Pepin, T. Km. N. 



Line. At. 42 (1889) 185-. 



2810 



Prime factors of integers. Loir, A. As. Fr. 



C. E. (1898) (Pt. 2) 144-. 

 , resolution of large numbers into. Pepin, 



T. Em. N. Line. At. 43 (1890) 163- ; Em. 



N. Line. Mm. 17 (1900) 321-. 

 , . Barbette, E. Mathesis 



19 (1899) 241-. 

 , , Euler's method. Pepin, 



T. Km. N. Line. Mm. 9 (1893) (Pt. 1) 47-. 

 , numbers into. Lucas, E. N. A. 



Mth. 14 (1875) 523-. 

 , . Landry, F. As. Fr. C. E. 



(1880) 185-. 



, 2 1 into. Gohierre de Long- 

 champs, . C. E. 85 (1877) 950-. 



number divides certain product of differences. 

 Grunert, J. A. Grunert Arch. 10 (1847) 302-. 



7, properties. Tucker, R. Nt. 40 (1889) 115-. 



p-\ i 



p, numerator of S - is divisible by p 2 . 



Wolstenholme, J. QJ. Mth. 5 (1862) 35-. 

 , theorem on sum of products divisible 



bjp. Steiner, J. Crelle J. 13 (1835) 356-. 

 , (Steiner). 



Jacobi, C. G. J. Crelle J. 14 (1835) 64-. 

 Primes. Tuxen, C. (xn) Ts. Mth. 5 (1881) 16-. 

 . Petersen, J. P. C. (xn) Ts. Mth. 6 



(1882) 138-. 



in arithmetical progression. Cantor, M. 

 Schlomilch Z. 6 (1861) 340-. 



, criteria. Thaarup, F. (xn) Ts. Mth. 5 



(1881) 77-. 



, . Zsigmondy, K. Mh. Mth. Ps. 5 (1894) 

 123-. 



of form 2n + 1, falsity of theorem in Gerg. ix 

 320. Sarrus, F. Gergonne A. Mth. 10 

 (1819-20) 184-. 



6m + 1. Krafft, W. L. [1798] St Pet. 



Ac. Sc. N. Acta 12 (1801) 217-. 

 100t + 1. Daublebsky von Sterneck, R. 



Wien Az. 31 (1894) 2-. 

 8m + 3, 8m + 7, 12m + 5, 12m + 7, etc. 



Iwanow, J. J. Fschr. Mth. (1899) 173. 

 , functions analogous to sine and cosine. 



Lucas, E. Tor. Ac. Sc. At. 11 (1875-76) 928-. 



occurring in arithmetical progressions. 

 Guibert, A. Liouv. J. Mth. 7 (1862) 414-. 



, properties. Lionnet, E. N. A. Mth. 1 



(1842) 175-. 

 , property. Bouniakowsky , V. St Pet. Ac. 



Sc. Bll. 4 (1838) 65-. 

 , theorems. Laisant, C. A. Bordeaux S. 



Sc. Mm. 1 (1876) 399. 



, . Ferrers, N. M. Mess. Mth. 23 (1894) 56-. 

 , (Ferrers). Rawson, R. Mess. Mth. 24 



(1895) 68-. 

 , theory. Baudrimont, A. Bordeaux Mm. 



S. Sc. 3 (cah. 2) (1865) 418-. 



of various linear forms. Liouville, J. Liouv. 

 J. Mth. 3 (1858) 84-; 4 (1859) 399-; 5 (1860) 

 103-, 119-, 139-, 300, 301-, 303-, 309-, 

 311-, 387-, 389-, 391- ; 6 (1861) 1-, 7-, 28-, 

 31-, 55-, 93-, 97-, 101-, 103-, 105-, 107-, 

 109-, 147-, 150-, 185-, 187-, 189-, 191-, 

 193-, 195-, 197-, 199-, 201- , 203-, 205-, 

 207-, 219- ; 7 (1862) 17-, 18-, 21-, 23-, 136 ; 

 8 (1863) 85-, 102-, 137- ; 9 (1864) 135-, 137- . 



196 



