Sttidi/ of Diophaniine Anahjsis in the United States. 45 



in the Mathmatical Visitor of 1880, and by A. L. Foot in the 

 School Mes^oi^/er (now Matlinvitical Mess:wjer), Vol. Ill, No. 8. 

 Dr. Martin published solutions of his own also in the Mathmatical 

 Vi.-^itor. In 1887 he read before the Philosophical Society of 

 "Washington a paper " On nth. Power Numbers Whose Sum is 

 an nth Power." 



In the Mathmatical Messenr/ev published by G. H. Harvill, 

 of Louisiana, indeterminate problems are solved by A. L. 

 Foote, B. F. Finkle, B. F. Burleson. In the School Visiior, 

 published by John S. Koyer, we have seen contributions of B. 

 F. Fiukel and D. H. Davison. 



A most interesting " Collection of Diophantine Problems 

 with Solutions, compiled by James Matteson, M. D., of De 

 Kalb Centre, Illinois," and published by Dr. Martin, 1888, 

 exhibits the results of DioiDhantine studies in this country at 

 their most advanced stage. The solutions of probloms 1 and 4 

 in this collection are by the late Abijah McClean, of New Lisbon, 

 Ohio; 5, 7, 9, 22, and 24 are from the pen of Dr. D. S. Hart; 

 6, 8, and 12 are by Dr. Matteson. The remaining solutions are 

 chiefly the work of Eeuben Davis, of Clifton, Kansas. A small 

 pamphlet giving " A Discussion of the equation h" = ir + If, 

 when h, p, h are Integer Numbers," by Josiah Scott, was pub- 

 lished at Bucyrus, Ohio, in 1871. 



Diophantine problems were such a favorits study that at one 

 time they found their way into some of our school-books. This 

 may have been done in imitation of English writers, such as 

 Bonn5^castle, whose little algebra was republished in this coun- 

 try. Charles W. Hackley, in his "Treatise on Algebra," 1846, 

 gives eleven pages to Diophantine Analysis and thirty-five 

 pages to the Theory of Numbers in which he introduces the 

 Gaussian notation for the treatment of congruent numbers. 

 Enoch Lewis has a chapter on indeterminate analysis in his 

 algebra. The key to Ray's Algebra devotes some space to our 

 topic. 



