Transcription of Elementary Number Theory - Joshua
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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:.. 3, 2, 1,0,1,2,3.. Although the integers are familiar, andtheir properties might therefore seem simple, it is instead a very deep example, here are some problems in Number Theory that remain unsolved.(Recall that aprime numberis an integer greater than 1 whose only positivefactors are 1 and the Number itself.)
1.1 Definition The number d divides the number n if there is a k such that n = dk. (Alternate terms are: d is a divisor of n, or d is a factor of n, or n is a multiple of d.) This relationship between d and n is symbolized d | n. The symbol d - n means that d does not divide n. Note that the symbol d | n is different from the fraction symbol ...
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