|
Derived from
|
20410627 TN410 - INTRODUCTION TO NUMBER THEORY in Mathematics LM-40 PAPPALARDI FRANCESCO
(syllabus)
Division, Factorization, Some Elementary Properties of Primes, Some Results and Problems Concerning Primes.
ARITHMETIC FUNCTIONS: The Divisor Function. The Moebius Function. The Euler Function. Dirichlet Convolution
CONGRUENCES: Sets of Residues,Some Interesting Congruences, Some Linear Congruences, Some Polynomial Congruences, Primitive Roots, the Theorem of Gauss.
QUADRATIC RESIDUES: The Legendre Symbol. Quadratic Reciprocity. The Jacobi Symbol.The Distribution of Quadratic Residues.
SUMS OF INTEGER SQUARES: Sums of Two Squares. Number of Representations. Sums of Four Squares. Sums of Three Squares.
ELEMENTARY PRIME NUMBER THEORY: Euclid's Theorem Revisited. The Von Mangoldt Function. Tchebycheff's Theorem. Some Results of Mertens
(reference books)
Chen, W; ELEMENTARY NUMBER THEORY. https://rutherglen.science.mq.edu.au/wchen/lnentfolder/lnent.html
Chowdhury, F.; Chowdhury, M. R. Essentials of Number Theory. Pi Publications, Dhaka, Bangladesh, 2005. ISBN 984-32-2836-7
Hardy, G. H.; Wright, E. M. An introduction to the theory of numbers. Fifth edition. The Clarendon Press, Oxford University Press, New York, 1979. xvi+426 pp. ISBN: 0-19-853170-2; 0-19-853171-0
Davenport, H. Aritmetica superiore. Un'introduzione alla teoria dei numeri. Editore: Zanichelli, 1994. 199 pp. ISBN: 8808091546
Gioia, A. A. The theory of numbers. An introduction. Reprint of the 1970 original. Dover Publications, Inc., Mineola, NY, 2001. xii+207 pp. ISBN: 0-486-41449-3
Rosen, K. H. Elementary number theory and its applications. Fourth edition. Addison-Wesley, Reading, MA, 2000. xviii+638 pp. ISBN: 0-201-87073-8
Tattersall, J. J. Elementary number theory in nine chapters. Cambridge University Press, Cambridge, 1999. viii+407 pp. ISBN: 0-521-58531-7
|
Università Roma Tre