## Introduction to Number TheoryA specific feature of this text on number theory is the rather extensive treatment of Diophantine equations of second or higher degree. A large number of non-routine problems are given. The book is intended for graduate students and research mathematicians. |

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according algebraic applying belongs bers called clearly coefficients complete conclude congruence consequence consider constant curve determined Diophantine equation distinct divides divisible easily equal exactly Example exist exponent expressed extended field Finally finite following theorem formula four function fundamental solution Further given greatest common divisor Hence holds hypothesis identical congruence incongruent solutions inequality infinitely integers integral polynomial interval lattice points least Lemma means method mod n modulo n multiple natural number obtain obviously odd prime points polynomial f positive positive divisors positive integers possible prime divisors prime factors primitive root problem Proof prove prove the following prove Theorem quadratic non-residue quadratic residue rational relation relatively prime represents result right-hand side rules satisfy Show solution solvable solving square Suppose Theorem theory tion true unit values written zero