An introduction to the theory of numbers
The Fifth Edition of one of the standard works on number theory, written by internationally-recognized mathematicians. Chapters are relatively self-contained for greater flexibility. New features include expanded treatment of the binomial theorem, techniques of numerical calculation and a section on public key cryptography. Contains an outstanding set of problems.
32 pages matching rational points in this book
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algebraic number arithmetic binary quadratic form calculate Chinese Remainder Theorem complete residue system complex numbers congruence f(x congruence x2 convergent deduce defined degree denote the number determine Dirichlet series distinct divides divisible elements elliptic curve equivalent Euclidean algorithm Euler's criterion example Farey sequence Fermat's finite follows formula function given greatest common divisor hence identity iff(U implies infinitely integral coefficients integral solution least positive Lemma Let f(x linear matrix modulo multiplicative nonzero number of solutions number theory odd prime pairs perfect square positive integer prime factor prime number primitive root primitive root mod probable prime proof of Theorem Prove pseudoprime quadratic nonresidue quadratic reciprocity quadratic residue rational numbers rational points real numbers reduced residue system relatively prime residue classes residue system modulo satisfying Section sequence Show Similarly solutions of x2 solvable square-free subsets Suppose unique values write zero