2800 



Theory of Numbers. General 



2800 



Equation ax 2 + bx + c = E fax* + b^x -f Cj) , so- 

 lution. Serdobinskil, V. E. (xn) Eec. Mth. 

 (Moscou) 7 (1874-75) (Ft. 1) 437- ; (xi) Bll. 

 Sc. Mth. As. 10 (1876) 103-. 



Euclidean numbers, so-called. Studnicka, F. J. 

 Prag Sb. (1899) (Mth.-Nt.) No. 30, 4 pp. 



proofs of theorems. (Product of two primes 

 by a third number is prime to the third, etc.) 

 Genocchi, A. N. A. Mth. 13 (1854) 426-. 



Integers are of form 

 4mra -m-n 



Euler, theorem. 



Genocchi, A. N. A. Mth. 12 (1853) 235-. 

 Even numbers. Studnicka, F. J. dasopis 



26 (1897) 207- ; Fschr. Mth. (1897) 164. 

 -- . ' ' Is every even number the sum of two 



odd primes?" Lionnet, E. N. A. Mth. 18 



(1879) 356-. 

 Every cube is difference of 2 squares, etc. 



Tait, P. G. [1870] Edinb. E. S. P. 7 (1872) 



144. 



integer divides a number expressed by 9's 

 followed by O's. Grunert, J. A. Crelle J. 

 5 (1829) 185-. 



-- power fj. of an integer I can be obtained 

 by taking the sum / of l k consecutive odd 

 numbers. Lemoine, E. N. A. Mth. 9 (1870) 

 368-. 



number is composed of 4 square numbers or 

 less, proof without primes. Pollock, (Sir) F. 

 [1851] E. S. P. 6 (1854) 132-. 



Farey's series. Lucas, E. [1877] Par. S. 



Mth. Bll. 6 (1878) 118-. 

 -- , series of fractions analogous to. Halphen, 



G. H. Par. S. Mth. Bll. 5 (1877) 170-. 

 Fermat, some problems. Pepin, T. Em. N. 



Line. Mm. 8 (1892) 85-. 

 Format's, Euler's, Wilson's, von ^Staudt's and 



Clausen's theorems. Lucas, E. Mathesis 



11 (1891) 9-. 



4th porism. Ofterdinger, (Dr) . Arch. 

 Mth. Ps. 46 (1866) 1-. 



numbers. Pollock, (Sir) F. [1866-68] E.S.P. 

 15 (1867) 115- ; Phil. Trans. 158 (1868) 627-. 



-- . Cunningham, (Lt.-Col.) A. B. A. Ep. 

 (1899) 653-. 



theorem, identity with fundamental property 

 of periodic fractions. Mansion, P. [1875] 

 Mess. Mth. 5 (1876) 33. 



Fifteen girl problem, cyclic solution. Peirce, B. 



Gould As. J. 6 (1861) 169-. 

 Formula, new. Cesdro, E. (xn) Mathesis 2 



(1882) 148-. 



2 2 + l. Pepin, T. C. E. 85 (1877) 329-. 



2 - 1. Pepin, T. C. B. 86 (1878) 307-. 

 Formulae, general. Liouville, J. Liouv. J. 



Mth. 3 (1858) 143-, 193-, 201-, 241-, 273-, 

 325- ; 4 (1859) 1-, 73-, 111-, 195-, 281- ; 5 

 (1860) 1-; 9 (1864) 249-, 281-, 321-, 389-; 

 10 (1865) 135-, 169-. 



, various. Cauchy, A. L. C. E. 12 (1841) 

 698-, 813-. 



Fourier' s series and a formula of Gauss. Hermite, 



C. Am. J. Mth. 9 (1887) 381-. 

 Fraction, division into sum of fractions with 



given denominators. Tirelli, F. G. Mt. 16 



(1878) 88-. 



Fractions arranged in order of magnitude, 



systematic interruption. Airy, G. B. Ph. 



Mg. 12 (1881) 175-. 

 , denominators of which >, theorem. 



Cauchy, A. L. Par. S. Phlm. Bll. (1816) 133-. 

 , irreducible, periods ; theorems of Lionnet's. 



Meyer, G. F. [1868] Arch. Mth. Ps. 49 



(1869) 168-. 

 , , series. Ocagne, M. d\ Brux. S. Sc. 



A. 10 (1886) (Pt. 2) 90-. 

 , number of, in any "Farey series" of which 



limiting number is given. Sylvester, J. J. 



Ph. Mg. 15 (1883) 251- ; 16 (1883) 230-. 

 , denominators and numerators of 



which do not exceed certain number. 



Sylvester, J. J. (xn) J. H. Un. Cir. [2] 



(1883) 44-. 

 , , formed with integers less than given 



number. Sylvester, J. J. C. E. 96 (1883) 



409- ; Mess. Mth. 27 (1898) 1-. 

 , property. Farey, J. Tilloch Ph. Mg. 47 



(1816) 385-. 

 , . Glaisher, J. W. L. Ph. Mg. 7 (1879) 



321-. 

 , tabulation of all, between given limits. 



Sang, E. [1878] Edinb. E. S. T. 28 (1879) 



287-. 

 Function E (f (x)) , modification ; quadratic and 



non quadratic residues of form 4/c + 1. 



Bunlakovskij, V. Ja. [1885] St Pet. Ac. Sc. 



Mm. (Rs.) 52 (1886) 124- ; Fschr. Mth. (1886) 



Functions arising in theory of numbers. Berger, 

 A. Stockh. Ofv. (1898) 579-. 



of even numbers, Laplace's method. Jacobi, 

 C. G. J. As. Nr. 28 (1849) 257-. 



in theory of numbers, general questions. 

 Bervi, N. V. [1894] Eec. Mth. (Moscou) 18 

 (1896) 519- ; Fschr. Mth. (1896) 156-. 



, present state of knowledge. 

 Bervi, N. V. Eec. Mth. (Moscou) 19 (1897) 

 182- ; Fschr. Mth. (1896) 156. 



General aspects of theory of numbers. Bourdat, 

 . Grenoble Ac. Delph. Bll. 3 (1850) 37-. 



remarks. Sludskti, T. A. [1864] (xn) Eec. 

 Mth. (Moscou) 2 (1867) (Ft. 2) 195-. 



Geometrical illustrations of some theorems. 



Davis, E. W. Am. J. Mth. 15 (1893) 84-. 

 Geometry, application to theory of numbers. 



Busche, E. Crelle J. Mth. 104 (1889) 32-. 



of numbers. Minkowski, H. D. Mth. Vr. 

 Jbr. 1 (1892) 64-. 



Goldbach's odd numbers. Stern, M. A. N. A. 

 Mth. 15 (1856) 23-. 



theorem, Euler's extension. Terquem, O. 

 N. A. Mth. 11 (1852) 326-. 



Hamiltonian differences, Sylvester's tables. 



Glashan, J. C. QJ. Mth. 27 (1895) 242-. 

 History, remarks. Henry, C. As. Fr. C. E. 



(1880) 201-. 

 Identities, numerical, etc. Serdobinskil, V. E. 



[1872] (xn) Eec. Mth. (Moscou) 6 (1872-73) 



(Pt. 1) 107-. 

 , , method of finding and application to 



theory of numerical functions. Baskakov, 



S. I. [1881] (xn) Eec. Mth. (Moscou) 10 



(1882-83) (Pt. 1) 313-. 



189 



