000			a
999			_c30922 _d30922
008			230212b xxu||||| |||| 00| 0 eng d
020			_a9781524948016
082			_a512.7 _bGAL
100			_aGallitano, Gail
245			_aTopics in number theory
260			_bKendall Hunt Publishing, _c2018 _aUSA :
300			_axi, 291 p. ; _bill. _c29 cm
365			_b176.40 _cUSD _d85.20
504			_aIncludes bibliographical references and index.
520			_a Topics in Number Theory is essentially a first course in number theory and as a prerequisite requires familiarity not much more than what is covered in any high school mathematics curriculum. This book is rich in examples. All the basic topic in elementary number theory including congruence, number theoretic functions, quadratic reciprocity, representation of certain primes in the form x2 + Ny2 using a theorem of Thue, continued fractions and Pell’s equation have been presented in appropriate details and illustrated by examples. Chakrav ala ‘Algorithm’ for finding a solution of Pell’s equation is also presented. The discussion of quadratic fields is followed by Euler’s proof of Fermat’s Last Theorem for exponent three. Several examples of Bachet equations having no solutions whose proofs can be provided based only on congruence arguments are discussed. The discussion of RSA cryptopgraphy is followed by an example using sufficiently large prime numbers. John Conway’s doomsday algorithm for finding day of the week is presented and is graphically illustrated by several examples. This book has over one hundred problems of various level of difficulty from very elementary to challenging. Hints of solutions have been provided to most of these problems.
650			_aNumber theory
650			_aAlgebraic number
650			_aAlgebraic Integer
700			_aGupta, Shiv
942			_2ddc _cBK