TY  - BOOK
AU  - Hill,Richard Michael
TI  - Introduction to number theory
T2  - Essential textbooks in mathematics
SN  - 9781786344717 (hc : alk. paper)
AV  - QA241 .H4845 2018
U1  - 512.7 H55 2018 23
PY  - 2018///
CY  - New Jersey, USA
PB  - World Scientific
KW  - Number theory
KW  - Textbooks
N1  - Textbook, with answers to some exercises; Includes bibliographical references; Machine generated contents note: 1.Euclid's Algorithm --
1.1.Some Examples of Rings --
1.2.Euclid's Algorithm --
1.3.Invertible Elements Modulo n --
1.4.Solving Linear Congruences --
1.5.The Chinese Remainder Theorem --
1.6.Prime Numbers --
Hints for Some Exercises --
2.Polynomial Rings --
2.1.Long Division of Polynomials --
2.2.Highest Common Factors --
2.3.Uniqueness of Factorization --
2.4.Irreducible Polynomials --
2.5.Unique Factorization Domains --
Hints for Some Exercises --
3.Congruences Modulo Prime Numbers --
3.1.Fermat's Little Theorem --
3.2.The Euler Totient Function --
3.3.Cyclotomic Polynomials and Primitive Roots --
3.4.Public Key Cryptography --
3.5.Quadratic Reciprocity --
3.6.Congruences in an Arbitrary Ring --
3.7.Proof of the Second Nebensatz --
3.8.Gauss Sums and the Proof of Quadratic Reciprocity --
Hints for Some Exercises --
4.p-Adic Methods in Number Theory --
4.1.Hensel's Lemma --
4.2.Quadratic Congruences --
4.3.p-Adic Convergence of Series Note continued: 4.4.p-Adic Logarithms and Exponential Maps --
4.5.Teichmuller Lifts --
4.6.The Ring of p-Adic Integers --
Hints for Some Exercises --
5.Diophantine Equations and Quadratic Rings --
5.1.Diophantine Equations and Unique Factorization --
5.2.Quadratic Rings --
5.3.Norm-Euclidean Quadratic Rings --
5.4.Decomposing Primes in Quadratic Rings --
5.5.Continued Fractions --
5.6.Pell's Equation --
5.7.Real Quadratic Rings and Diophantine Equations --
Hints for Some Exercises --
Solution to Exercises; CoED; Bachelor of Secondary Education major in Mathematics
ER  -