000			nam a22 4500
999			_c32636 _d32636
008			231129b xxu||||| |||| 00| 0 eng d
020			_a9783030081300
082			_a510 _bGRI
100			_aGrigorieva, Ellina
245			_aMethods of Solving Number Theory Problems
260			_bBirkhauser, _c2018 _aCham :
300			_axxi, 391 p. ; _bill., _c23 cm
365			_b49.99 _cEUR _d91.70
504			_aIncludes index.
520			_aThrough its engaging and unusual problems, this book demonstrates methods of reasoning necessary for learning number theory. Every technique is followed by problems (as well as detailed hints and solutions) that apply theorems immediately, so readers can solve a variety of abstract problems in a systematic, creative manner. New solutions often require the ingenious use of earlier mathematical concepts - not the memorization of formulas and facts. Questions also often permit experimental numeric validation or visual interpretation to encourage the combined use of deductive and intuitive thinking. The first chapter of the book covers topics like even and odd numbers, divisibility, prime, perfect, figurate numbers, and introduces congruence. The next chapter works with representations of natural numbers in different bases, as well as the theory of continued fractions, quadratic irrationalities, and also explores different methods of proofs. The third chapter is dedicated to solving unusual factorial and exponential equations, Diophantine equations, introduces Pell's equations and how they connect algebra and geometry. Chapter 4 reviews Pythagorean triples and their relation to algebraic geometry, representation of a number as the sum of squares or cubes of other numbers, quadratic residuals, and interesting word problems. Appendices provide a historic overview of number theory and its main developments from ancient cultures to the modern day. Drawing from cases collected by an accomplished female mathematician, Methods in Solving Number Theory Problems is designed as a self-study guide or supplementary textbook for a one-semester course in introductory number theory. It can also be used to prepare for mathematical Olympiads. Elementary algebra, arithmetic and some calculus knowledge are the only prerequisites. Number theory gives precise proofs and theorems of an irreproachable rigor and sharpens analytical thinking, which makes this book perfect for anyone looking to build their mathematical confidence.
650			_aPythagorean triples
650			_aPell’s equation
650			_aLegendre symbol
650			_aJacobi symbol
650			_aFermat’s Little Theorem
650			_aDiophantine equations
650			_aCatalan number
942			_2ddc _cBK