Chap. XII] CrITEEIA FOR DIVISIBILITY. 345 
C. M. Ingleby for d = 9, 11, British Assoc. Report, 35, 1865, 7 (trans.). 
M. Jenkins for any prime d, Math. Quest. Educ. Times, 8, 1868, 69, 111. 
F. Unferdinger [Gergonnei^], Sitzungsber. Ak. Wiss. Wien (Math.), 59, 1869, II, 
465-6. 
H. Anton for d = 9, 11, 13, 101, Archiv Math. Phys., 49, 1869, 241-308. 
W. H. Walenn, British Assoc. Report, 40, 1870, 16-17 (trans.); Phil. Mag., (4), 
36, 1868, 346-8; (4), 46, 1873, 36-41; (4), 49, 1875, 346-351; (5), 2, 1876, 
345; 4, 1877, 378; 9, 1880, 56, 121, 271. 
M. A. X. Stouff for d< 100, Nouv. Ann. Math., (2), 10, 1871, 104. 
J. Lubin, ibid., (2), 12, 1874, 528-30 (trivial). 
Szenic for d = 7, 9, 37, Von der Kongruenz der Z., Progr. Schrimm, 1873. 
E. Brooks for d = 7, Des Moines Analyst, 2, 1875, 129. 
W. J. Greenfield and M. Collins for d = 47, 73, Math. Quest. Educ. Times, 22, 
1875, 87. 
F. da Ponte Horta for d = 7, 9, 11, 13, Jornal de Sciencias Mat. Ast., 1, 1877, 57-62. 
Mennesson for d = 7, Nouv. Corresp. Math., 4, 1878, 151; generahzation by Cesaro, 
p. 156. 
C. Lange, for d = 7, 13, 17, 19, Ueber die Teilbarkeit der Zahlen, Progr., Berlin, 1879. 
F. Jorcke for d = 7, 9, 11, Ueber Zahlenkongruenzen . . ., Progr, Fraustadt, 1878. 
K. Broda for any base, Archiv Math. Phys., 63, 1879, 413-428. 
A. Badoureau for d = 19, Nouv. Ann. Math., (2), 18, 1879, 35-6. 
S. M. Drach for d = 7, Math. Quest. Educ. Times, 35, 1881, 71-2. 
W. A. Pick for d = 7, ibid., 38, 1883, 64. 
A. Evans for d = 7, Des Moines Analyst, 10, 1883, 134. 
K. Haas, Theilbarkeitsregeln . . ., Progr., Wien, 1883. 
G. Wertheim, Elemente der Zahlentheorie, 1887, 31-33. 
B. Adam for d<100, Ueber die Teilbarkeit. . ., Progr. Gym. Clausthal, 1889. 
A. Loir for d<138. Jour, de math, elem., 1889, 66, 107-10, 121-3. 
A. G. Fazio [SchlegeP^], Sui caratteri. . ., Palermo, 1889. 
E. Gelin, Mathesis, (2), 2, 1892, 65, 93; (2), 12, 1902, 65-74, 93-99 (extract in 
Mathesis, (3), 10, 1910, Suppl. I); Ann. Soc. Sc. Bruxelles, 34, 1909-10, 66; 
Recueil de problemes d'arith., 1896. Extracts by M. Nasso, Revue de Math. 
(ed., Peano), 7, 1900-1, 42-52. 
Speckmann, Dorsten, Haas, Dorr, Zeitschrift Math. Phys., 37, 1892, 58, 63, 
128, 192, 383. 
Lalbaletrier, Jour, de Math, (ed., de Longchamps), 1894, 54. 
H. T. Burgess [Pascal*], Nature, 57, 1897-8, 8-9, 30, 55. 
A. Conti [Pascal*], Periodico di Mat., 13, 1898, 180-6, 207-9. 
F. Mariantoni, ibid., 149-151, 191-2, 217-8. 
T. Lange for d<30, Archiv. Math. Phys., (2), 16, 1898, 220-3. 
W. J. Greenstreet, Math. Gazette, 1, 1900, 186-7. 
Christie for d = 2^p,5'^p (p prime). Math. Quest. Educ. Times, 73, 1900, 119. 
A. Cunningham and D. Biddle for d = rp=i=l, ibid., 75, 1901, 49-50. 
M. Zuccagni for d = 7, Suppl. al Periodico di Mat., 6, fasc. V. 
Calvitti for d = 7, ibid., 8, fasc. IV. 
S. Dickstein, Wiad. Mat., Warsaw, 6, 1902, 253-7 (Pohsh). 
B. Niewenglowski, ibid., 252-3. 
Pietzker ford = 7, 11, 13, 27, 37, Unterrichtsblatter Math. Naturwiss., 9, 1903, 
85-110. 
A. Church for d = 7, 13, 17, Amer. Math. Monthly, 12, 1905, 102-3. 
E. A. Cazes, Assoc, frang., 36, 1907, 55-63. 
A. Gerardin for d = 7, 13, 17, 37, 43, Sphinx-Oedipe, 1907-8, 2. 
M. Morale for d = 7, Suppl. al Periodico di Mat., 11, 1908, 103. 
*T. Ghezzi, ibid., 12, 1908-9, 129-130. 
Lenzi, II Boll. Matematica Gior. Sc.-Didat., 7, 1908. 
