2800 



Theory of Numbers. General 



2800 



Perfect number, odd, cannot have less than 

 five distinct prime divisors. Sylvester, J. J. 

 C. R. 106 (1888) 522-. 



numbers. Lebesgue, V. A. N. A. Mth. 3 

 (1844) 552-. 



. Lionnet, E. N. A. Mth. 18 (1879) 306-. 



. Lucas, E. Mathesis 6 (1886) 145-. 



. Novarese, H. G. Teix. J. Sc. 8 (1887) 



.' Sylvester, J. J. C. E. 106 (1888) 403-, 



641- ; Mathesis 8 (1888) 57-. 

 . Servais, C. Mathesis 8 (1888) 92-, 



135. 



. Catalan, E. Mathesis 8 (1888) 112-. 



. Lucas, E. Mathesis 10 (1890) 74-. 



. Bourlet, C. N. A. Mth. 15 (1896) 297-. 



. Pepin, T. Em. N. Line. Mm. 13 



(1897) 345-. 

 , history. Curtze, M. Bb. Mth. (1895) 



39-. 

 , properties of analogous numbers. Mlnln, 



A. P. [1882] (xn) Eec. Mth. (Moscou) 10 



(1882-83) (Pt. 1) 87-. 

 , theory. Carvallo, J. C. E. 81 (1875) 



73-. 

 Periods, law. Jonquieres, E. de. C. E. 96 



(1883) 1020-, 1129-, 1210-. 

 Permutations, circular, applications. Mac- 



Mahon, P. A. L. Mth. S. P. 23 (1892) 



305-. 

 Powers, difference of consecutive. Tronsens, 



A. N. A. Mth. 19 (1860) 310-. 



of number. Anon, (vi 886) N. A. Mth. 

 13 (1854) 424-. 



Primes. Laurent, H. N. A. Mth. 18 (1899)234-. 

 , characteristic relations for. Hacks, J. 

 Acta Mth. 17 (1893) 205-. 



of definite forms. Bang, A. S. N. Ts. 

 Mth. 2 (B) (1891) 73-; Fschr. Mth. (1891) 

 183. 



, determination of certain. Lawrence, F. W. 

 L. Mth. S. P. 28 (1897) 465-. 



equal to sums or differences of squares or 

 multiples of squares. Voiles, F. (xi) Par. 

 S. Phlm. Bll. 7 (1871) 191-. 



, expression in terms of preceding primes. 



Isenkrahe, C. Mth. A. 53J1900) 42-. 

 , forms arising from (a + v/6) k. Genocchi, A. 



A. Mt. 2 (1868-69) 256-. 

 , general formula. Dormoy, E. C. E. 63 



(1866) 178- . 

 , geometrical interpretation. Cassani, P. 



Yen. I. At. (1896-97) 103-. 

 , roots. Oltramare, G. Crelle J. 45 (1853) 



303-. 

 , theorems. Levi, G. Yen. I. At. (1892- 



93) 1816-. 

 , , enunciation. Proth, F. C. E. 83 (1876) 



1288-. 

 , theory. La Vallee-Poussin, C. J. de. Brux. 



S. Sc. A. 20 (1896) (Pt. 1) 100-, (Pt. 2) 183-, 



281- ; 21 (1897) (Pt. 1) xxiii, 1-, 60-, (Pt. 2) 



251-. 



Primitive numbers (not containing square fac- 

 tors), distribution. Bougaev, . C. E. 74 



(1872) 449-. 

 , properties. Maria, P. C. G. Mt. 4 



(1866) 345-. 



new laws. Coninck, G. de. N. A. Principles, first. Skrivan, G. Wien Jbr. 



Ober-Eealsch. Inn. Stadt 2 (1860) 1-. 

 , fundamental. Poinsot, L. C. E. 12 (1841) 



803- ; Liouv. J. Mth. 10 (1845) 1-; Grunert 



Arch. 7 (1846) 367-. 

 , (Poinsot). Grunert, J. A. Grunert 



Arch. 7 (1846) 168-. 

 Problem : to find several consecutive cubes 



whose sum is a square. Catalan, E. C. 



Brux. Ac. Bll. 22 (1866) 339-. 

 Problems, numerous. Gelin, E. Mathesis 16 



(1896) (Suppl.) 34 pp. 

 Products of digits of certain numbers. Sanctts, 



P. de. Em. N. Line. At. 52 (1899) 58-; 53 

 (1900) 57-. 

 and series involving prime numbers only. 



Glaisher, J. W. L. QJ. Mth. 27 (1895) 270- ; 



28 (1896) 1-. 

 Progressions, application. Volpicelli, P. Tor- 



tolini A. 5 (1854) 449-. 



Properties of integers derived from space in- 

 tuitions. Minkowski, H. N. A. Mth. 15 



(1896) 394-. 

 numbers. Vince, S. [1810] Ir. Ac. 



T. 12 (1815) 34-. 



. Anon. (vi319) Dingier 34 (1829) 68. 



. Perkins, G. B. Silliman J. 40 



(1841) 112-. 

 . Whitworth, W. A. QJ. Mth. 6 



(1863) 163-. 

 . Valat , J. P. F. Bordeaux Ac. Act. 



38 (1877) 73-. 

 . Torelli, G. G. Mt. 16 (1878) 152-. 



Mth. 13 (1874) 568-. 

 , properties. 0., D. QJ. Sc. 5 (1818) 



55-. 

 , relations. Prouhet, E. C. E. 33 



(1851) 225. 



, remainders. Buttel, P. Grunert 

 Arch. 26 (1856) 241-. 



, theorem. Fregier, . Gergonne 

 A. Mth. 9 (1818-19) 211-. 



, theorems. Terquem, 0. N. A. Mth. 5 



(1846) 70-. 



, uses in mechanics. Noel, J. N. 

 Quetelet Cor. Mth. 1 (1825) 124-, 199- 



whose sum is same power of some 

 number. Martin, Art. QJ. Mth. 26 (1893) 

 225-. 



, relations. Marchand, D. Les Mondes 44 

 (1877) 424-. 



and their differences. Kirwan, B. [1809] 

 Ir. Ac. T. 11 (1810) 131-. 



of 2 and 3. Sludskii, T. A. [1869] (xn) 

 Eec. Mth. (Moscou) 4 (1869-70) (Pt. 2) 171-. 



5 and their multiples. Berdelle, C. As. 



Fr. C. E. 8 (1879) 176-. 

 Prime of form 8n + l, theorem. Stern, M. A. 



Crelle J. 32 (1846) 89-. 

 , formation from lower primes. Scherk, H. F. 



Crelle J. 10 (1833) 201-. 



greater than given prime. Boije af Gennds, 

 C. 0. Stockh. Ofv. (1893) 469-. 



, theorem of Legendre. Pepin (le pere), T. 

 Liouv. J. Mth. 5 (1879) 21-. 



191 



