After successful completion of the course, students are able to

• explain divisibility properties of integers and to deduce main properties like the Fudamental Theorem of Number Theory,

• define and to apply number theoretic functions,

• use and to apply congruences,

• explain the theory of quadratic residues and to deduce their mein properties

• formulate important properties of prime numbers, to apply them, and to sketch their proofs,

• identfy several simple classes of Diophantine equation and to apply corresponding soltuion methods, and
  

• to sketch the ideas and methods that are needed to proof the main theorems.

Divisibility, number-theoretic functions, congruences, quadratic residues, prime numbers, diophantine equations

Blackboard lecture

Nebem den Skelettskriptum

https://owncloud.tuwien.ac.at/index.php/s/lxlKegGxM7b0Hrs

werden laufend Vorlesungsvideos zur Verfügung gestellt:

1. Teilbarkeit in ganzen Zahlen [Folien: https://owncloud.tuwien.ac.at/index.php/s/FhAp7xSuIWzPfPH]

1.1. ggT und kgV: https://owncloud.tuwien.ac.at/index.php/s/MoNgwkJmdbPg4dm
1.2. Fundamentalsatz der Zahlentheorie: https://owncloud.tuwien.ac.at/index.php/s/REy6HMnrYT1xatE
1.3. Gaußsche ganze Zahlen https://owncloud.tuwien.ac.at/index.php/s/I1ECcKWAKl5iwNP

2. Kongruenzen [Folien: https://owncloud.tuwien.ac.at/index.php/s/7tEXnYUO8rdUN28 ]

2.1. Eulersche phi-Funktion https://owncloud.tuwien.ac.at/index.php/s/0yWOE1wsxXCVtf2
2.2. Chinesicher Restsatz https://owncloud.tuwien.ac.at/index.php/s/zWYivBo9jeSQmHo
2.3. Primitivwurzeln https://owncloud.tuwien.ac.at/index.php/s/Os9m9cTg8q2pVap
2.4. Polynomiale Kongurenzen https://owncloud.tuwien.ac.at/index.php/s/EYfds6QCVJWkwFJ

3. Quadratische Reste  [Folien  https://owncloud.tuwien.ac.at/index.php/s/stI2vtlvVrSNkgF ]

3.1. Das Legendresymbol https://owncloud.tuwien.ac.at/index.php/s/42OS773WC2vQEZI
3.2. Das quadratische Reziprozitätsgesetz https://owncloud.tuwien.ac.at/index.php/s/AoSSFZPatqmH63b
3.3. Das Jacobisymbol https://owncloud.tuwien.ac.at/index.php/s/R4Q2GQIEUoPFXXD

4. Diophantische Gleichungen  [Folien https://owncloud.tuwien.ac.at/index.php/s/GPafL2AYQtldnDD  ]

4.1. Lineare Diophantische Gleichungen https://owncloud.tuwien.ac.at/index.php/s/sXla99BrfHP1Nys
4.2. Quadratische Diophantische Gleichungen https://owncloud.tuwien.ac.at/index.php/s/dOngwmgJnl9B6Ck
4.3. Die Pellsche Gleichung https://owncloud.tuwien.ac.at/index.php/s/Q3h9KKmAhXxbfJO
4.4. Summen von Potenzen https://owncloud.tuwien.ac.at/index.php/s/xNp4G8lwSBNJrit

5. Kettenbrüche  [Folien:  https://owncloud.tuwien.ac.at/index.php/s/ZVFdxT5WFxB8Jzv ]
5.1. Kettenbruch einer reellen Zahl  https://owncloud.tuwien.ac.at/index.php/s/5FUfV14l76JzjXc
5.2. Approximationseigenschaften von Kettenbrüchen https://owncloud.tuwien.ac.at/index.php/s/stnqpvTQ1VErHlD
5.3. Spezielle Kettenbrüche  https://owncloud.tuwien.ac.at/index.php/s/DlIlp9QcnGQo6Kj

Weiters finden regelmäßig Zoom-Fragestunden statt:

Fr: 26.3.21, 14 h: https://tuwien.zoom.us/j/92619428558
Fr. 16.4.21, 14 h:  https://tuwien.zoom.us/j/91416973616
Fr. 7.5.21, 14 h: https://tuwien.zoom.us/j/99557855262
Fr. 28.5.21, 14 h: https://tuwien.zoom.us/j/92346673893

Oral Exam.

Lecture notes for this course are available. http://www.dmg.tuwien.ac.at/drmota/