2800 



Theory of Numbers. General 



Properties of numbers. Dostor,G. Arch. Mth. 



Ps. 63 (1879) 221-. 

 . Pepin, T. C. E. 120 (1895) 1254-. 



, theorem. Ingleby, C. M. Mess. 

 Mth. 3 (1866) 30-. 



Property of numbers. H 'eider, M. Haidinger 



B. 1 (1846) 186. 



. Midy, . N. A. Mth. 5 (1846) 640-. 



. Dostor, G. J. N. A. Mth. 8 (1849) 



101-. 

 . Volpicelli, P. Em. At. 6 (1852-53) 



631. 

 . Genocchi, A. Brux. Ac. Bll. 20 



(1853) (pte. 2) 397-. 



. Booth, J. E. S. P. 7 (1854-55) 42-. 



. Anon, (vi 314) Crelle J. 50 (1855) 



187-. 



. Boncompagni, B. Tortolini A. 6 

 (1855) 371-. 



- in theory of numbers. Earnshaw, S. (vi 



Adds.) Camb. Mth. J. 2 (1841) 79-. 

 Propositions, miscellaneous. Cauchy, A. L. 



C. E. 24 (1847) 996-; 25 (1847) 132-, 177-, 

 242-. 



, . Catalan, E. C. N. A. Mth. 13 (1874) 



518-. 

 , . Thue,A. Arch. Mth. Ntvd. 16 (1893) 



255-; 19 (1897) No. 4, 27 pp.; Fschr. Mth. 



(1897) 165. 

 Eeal representation of imaginary configurations, 



and application to theory of numbers. Busche, 



E. Crelle J. Mth. 122 (1900) 227-. 

 Eeciprocals of primes. Goodwyn, H. Nichol- 

 son J. 4 (1801) 402-. 

 Eemainder as function of divisor and dividend. 



Schli'milch, 0. Grunert Arch. 10 (1847) 



424-. 

 Eepresentation of number in form Sa r n . 



Lemoine, E. As. Fr. C. E. (1900) (Pt. 2) 72-. 

 Eesidues of recurring series with regard to 



prime modulus. Mantel, W. N. Arch. 



Wisk. 1 (1895) 172- ; Fschr. Mth. (1893-94) 



423-. 

 Ehythmomachy, an ancient game. Terquem, 



0. N. A. Mth. 5 (1846) 662-. 

 Boots of numbers. Sanchis-Barrachina, E. 



N. A. Mth. 8 (1869) 265-. 

 Series involving inverse even powers of subeven 



and supereven numbers. Glaisher, J. W. 



L. Mess. Mth. 23 (1894) 176-. , 



of natural numbers. Collignon, E. As. Fr. 

 C. E. (1896) (Pt. 2) 17-. 



, number occupying given place. 



Barbier, E. C. E. 105 (1887) 795-, 1238-. 

 , . Ocagne, M . d' . C. E. 



106 (1888) 190-. 

 , problems. Bertrand, J. N. A. 



Mth. 8 (1849) 354-. 

 odd numbers, theorems. Selle, (le vicomte) 



de. Aix Ac. Mm. 18 (1900) 75-. 

 primes, and resolution of number into 



factors. Gough, J. Nicholson J. 1 (1802) 1-. 



in which coefficients are sums of divisors 

 of exponents, powers of. Glaisher, J. W. L. 

 Mess. Mth. 15 (1886) 33-. 



, square of. 



Glaisher, J. W. L. Mess. Mth. 14 (1885) 156-. 



2800 



Series + ! + i4-f + T 1 r+"- (primes) . Glaisher, 

 J. W. L. QJ. Mth. 25 (1891) 369-. 



i- t + f + T*r-Tir - (primes). Glaisher, 

 . W. L. QJ. 



. 



. Mth. 25 (1891) 375-. 



Glaisher > 



W. L. QJ. Mth. 26 (1893) 33-. 



i+i-t + A -A + . Glaisher, J. W. L. 

 QJ. Mth. 26 (1893) 48-. 



Sets of integers, determinant of which is > or 



< 1. Hermite, C. Liouv. J. Mth. 14 (1849) 



21-. 

 Square array of 16 numbers satisfying 22 con- 



ditions. Lebesgue, V. A. N. A. Mth. 15 



(1856) 403-. 



numbers, analysis. Wheeler, A. D. Silli- 

 man J. 25 (1834) 87-. 



-- , and biquadrates, ascertaining by inspec- 

 tion. Saint, W. Nicholson J. 22 (1809) 291-. 



-- , properties. Hoyt, D. H. Camb. (M.) 

 Mth. M. 3 (1860) 2-. 



-- , tables giving sets of final digits. Schady, 

 . Crelle J. Mth. 84 (1878) 85-. 



that are sums of squares. Martin, A. 

 Wash. Ph. S. Bll. 11 (1892) 580-. 



Squares, theorems of 2, 4, 8, 16. Cayley, A. 



QJ. Mth. 17 (1881) 258-. 

 Sum and difference of two squares. Claude, 



R. P. L. N. A. Mth. 2 (1863) 88-. 



of Jith powers of numbers < and prime 

 to n. Thatker, A. Crelle J. 40 (1850) 89-. 



reciprocals of like powers of primes, 

 theorem. GlaisJier, J. W. L. As. Fr. C. E. 

 6 (1877) 172-. 



series 2 z , p being prime number. 



Glaisher, J. W. L. Mess. Mth. 7 (1878) 190-. 

 Sums of inverse powers of primes. Glaisher, 

 J. W. L. QJ. Mth. 25 (1891) 347-. 



. like powers of prime numbers. Bour, 

 J. E. E. Par. S. Phlm. Bll. 2 (1865) 8-. 



series of reciprocals of primes and of 

 their powers. Merrifield, C. W. [1881] 

 E. S. P. 33 (1882) 4-. 



squares, relations. Dostor, G. Arch. 

 Mth. Ps. 67 (1882) 265-. 



--- , theorems. Realis, S. N. A. Mth. 

 12 (1873) 212- ; 18 (1879) 500-. 



three squares. Dainelli, U. G. Mt. 

 15 (1877) 378-. 



, value of some. Stern, M. A. Gott. Ab. 

 17 (1872) (Mth.) 63-. 



Tables of uniform reversible functions of two 

 variables on the simplest number-domains. 

 Schroder, E. Mth. A. 29 (1887) 299-. 



Theorems, Berger's, proof and generalisation. 

 Cesdro, E. (xn) Mathesis 1 (1881) 99-. 



, various. Talbot, W. H. F. [1862] Edinb. 

 E. S. T. 23 (1864) 45-. 



, . Gegenbauer, L. Wien Ak. D. 49 (1885) 

 (Ab. 1) 1-, (Ab. 2) 105- ; 57 (1890) 497-; 

 60 (1893) 25-. 



, . Catalan, E. Brux. Ac. Mm. 46 (1886) 

 No. 1, 16 pp. 



Theory of numbers and automorphic functions, 

 relations. Fricke, R. D. Mth. Vr. Jbr. 

 (1899) (Heft 1) 94-. 



192 



