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Elementary Number Theory - Joshua

Elementary Number TheoryA revision by Jim Hefferon, St Michael s College, 2003-Decof notes by W. Edwin Clark, University of South Florida, 2002-DecLATEX source compiled on January 5, 2004 by Jim restriction claimed by W. Edwin 2002: Copyleftmeans thatunrestricted redistribution and modification are permitted, provided that all copiesand derivatives retain the same permissions. Specifically no commerical use of thesenotes or any revisions thereof is permitted. iiPrefaceMathematics is the queen of sciences andarithmetic the queen of mathematicsCarl Friedrich GaussNumber Theory , known to Gauss as arithmetic, studies the properties of theintegers.

Number theory, known to Gauss as “arithmetic,” studies the properties of the integers: ... − 3,−2,−1,0,1,2,3.... Although the integers are familiar, and their properties might therefore seem simple, it is instead a very deep subject. For example, here are some problems in number theory that remain unsolved.

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