2800 



Theory of Numbers. General 



Inequalities relating to prime numbers. Syl- 

 vester, J. J. Nt. 38 (1888) 259-. 

 Infinite series, use in theory of numbers. 



Lejeune-Dirichlet, G. Crelle J. 18 (1838) 



259-. 

 Infinitesimal analysis, applications to theory of 



numbers. Lejeune-Dirichlet, G. Crelle J. 



19 (1839) 324-; 21 (1840) 1-, 134-. 

 Integers of certain form. Rocquigny, F. [G.~] de. 



Les Mondes 53 (1880) 410-. 

 , property of a certain series. Sylvester, J. J. 



C. E. 88 (1879) 1297-. 

 , solutions by. Liouville, J. Liouv. J. Mth. 



4 (1859) 271-. 

 , successions that cannot be indefinitely 



continued. Sylvester, J. J. [1882] (xn) 



J. H. Un. Cir. [2] (1883) 2-. 

 , systems. Cesdro, E. Km. E. Ac. Line. 



Ed. 4 (1888) (Sem. 1) 457-. 

 , theorem. Serret, J. A. Liouv. J. Mth. 13 



(1848) 12-. 

 , . Durege, . Grunert Arch. 30 (1858) 



163-. 

 , (Durege). Lottner, C. L. E. Grunert 



Arch. 32 (1859) 111-. 

 , theory. Binet, J. P. M. Liouv. J. Mth. 6 



(1841) 449-. 

 Integral calculus, applications. Lucas, E. C. 



E. 82 (1876) 1303-. 



, . Weber, H. Gott. Nr. (1896) 275-. 



Latent integer, formal property. Sylvester, J. J. 



QJ. Mth. 1 (1857) 185. 

 Laws of numbers, problems. Marchand, D. 



Les Mondes 38 (1875) 460- ; 39 (1876) 26-, 



346-, 693-. 

 Legendre's functions, application. Bauer, G. 



Munch. Ak. Sb. 24 (1895) 343-. 

 Linear modular system, reduction. Fund, 0. 



Hamb. Mth. Gs. Mt. 3 (1900) 423-. 

 with root of product of MI numbers. Boutroux, 



. N. A. Mth. 1 (1842) 368-. 

 Maximum product of components. Derbes, J. 



N. A. Mth. 19 (I860) 117-. 

 Mean values in theory of numbers. Lejeune- 

 Dirichlet, G. Berl. Ab. (1849) (Mth.) 69-. 

 . Berger,A. Ups. S. Sc. N. 



Acta 14 (1891) No. 2, 130 pp. 

 Miscellaneous notes. Catalan, E. As. Fr. C. 



E. (1891) (Ft. 2) 194-. 

 nth powers that are sums of nth powers. 



Martin, A. Smiths. Misc. Col. 33 (1888) 



Art. 4, 107-. (Wash. Ph. S. Bll. 10 



(1888).) 

 Nasik cubes. Trost, A. H. QJ. Mth. 8 (1867) 



74. 

 , general properties. Frost, A. H. [1877] 



QJ. Mth. 15 (1878) 93-, 366-. 

 squares, general properties. Frost, A. H. 



[1877] QJ. Mth. 15 (1878) 34-. 

 Natural system of numbers. Pujols de la Bas- 



tida, V. Madrid Ev. 4 (1854) 567-; 5 (1855) 



436-. 

 Nature and properties of numbers. Jamard, . 



Eouen Tr. Ac. (1804) 75-. 

 New basis for a general theory. Kraus, J. 



Z. Mth. Ps. 37 (1892) 321- ; 39 (1894) 11-. 

 Number equal to sum of p squares, certain. 

 Catalan, E. C. (xn) Mathesis 3 (1883) 199. 



2800 



Number, prime or composite, test. Koch, H. 

 von. Stockh. Ofv. (1900) 789-. 



of times a prime is contained in product of 

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 185-. 



3, properties. Gegenbauer, L. Wien Ak. 

 Sb. 97 (1889) (Ab. 2a) 271-. 



5 and number 7, characteristic properties. 

 Lucas, E. N. A. Mth. 18 (1879) 74-. 



60, characteristic. Wasserschleben, von. 

 Arch. Mth. Ps. 54 (1872) 411-. 



107| property. Schwering, K. Acta Mth. 

 11 (1887-88) 119-. 



Numbers, class. Collignon, E. As. Fr. C. E. 



(1895) (Ft. 2) 6-. 

 , classes, two. Debacq, C. Les Mondes 29 



(1872) 308-. 

 , elementary theorems. Chabert, . N. A. 



Mth. 3 (1844) 250-. 



of form 4m + 1, theorem. Liouville, J. 

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, (Liouville). Zolotareff, G. 



[1870] St. Pet. Ac. Sc. Bll. 16 (1871) 



85-. 

 , ( ). Pepin, T. Em. N. Line. 



Mm. 5 (1889) 131-. 

 , four, in arithmetical progression of which 3 



are squares. Guibert, A. N. A. Mth. 1 



(1862) 249-. 

 , problems. Noel, J. N. Liege Mm. S. Sc. 



4 (1847) 55-. 

 , series and equations. Grolous, J. (x) Par. 



S. Phlm. Bll. 8 (1872) 119-. 



with a single arbitrary function, general 

 theorem. Bugaev, N. V. [1865] (xn) 

 Eec. Mth. (Moscou) 2 (1867) (Ft. 1) 10-. 



, succession of 2n + l, so that sum of squares 



of first n + l = that of last n. Dostor,G. Arch. 



Mth. Ps. 64 (1879) 350-. 

 , three, such that sum or difference of any 



two is square. Euler, L. [1780] St. Pet. 



Ac. Sc. Mm. 6 (1818) 54-. 

 Odd and even numbers. Martin, Art. Des 



Moines Anal. 2 (1875) 20-. 

 , theorem of Gauss. Stern, M. A. 



Gott. Nr. (1869) 330-. 



numbers, theorems on two. Catalan, E. C. 

 Liege S. Sc. Mm. 6 (1877) No. 4, 4 pp. 



, Turner's property. Grunert, J. A. 

 Grunert Arch. 1 (1841) 59-. 



. , . Hellerung, . Grunert Arch. 1 



(1841) 318-. 

 Origin and development of theory of numbers. 



StudniSka, F. J. Casopis 4 (*1874) 1-. 

 Partition analysis applied to properties of any 



system of consecutive integers. MacMahon, 



P. A. [1899] Camb. Ph. S. T. 18 (1900) 



12-. 



of even number into two primes. Sylvester, 

 J. J. [1871] L. Mth. S. P. 4 (1871-73) 4-. 



<t>(P n ) an< l 0(2p n ) P being a prime. 



Sancery, L. [1875] Par. S. Mth. Bll. 4 



(1876) 17-. 

 Perfect cubes. Henkle, W. D. Des Moines 



Anal. 1 (1874) 75- ; 2 (1875) 65-. 

 . Sensenig, D. M. Des Moines Anal. 3 



(1876) 104-. 



190 



