02878nam 2200265 4500999001700000008004100017020001800058082001300076100002300089245004600112260003000158300003200188365002200220504002000242520204100262650002402303650003002327650002002357650001802377650003802395650002602433650001902459942001202478952012202490 c32636d32636231129b xxu||||| |||| 00| 0 eng d a9783030081300 a510bGRI aGrigorieva, Ellina aMethods of Solving Number Theory Problems bBirkhauser,c2018aCham : axxi, 391 p. ;bill.,c23 cm b49.99cEURd91.70 aIncludes index. 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. aPythagorean triples aPell$1 (Bs equations aLegendre symbol aJacobi symbol aFermat$1 (Bs Little Theorems aDiophantine equations aCatalan number 2ddccBK 00102ddc406510_000000000000000_GRI70942894aDAIICTbDAIICTd2023-11-25g4584.08o510 GRIp034490r2023-11-29yBK