Number Theory
Semester II (PS02EMTH53)
same as Sem I (PS01EMTH53)
Syllabus
| Unit-I | The division algorithm, the greatest common divisor, the Euclidean algorithm, the fundamental theorem of arithmetic, infinitude of prime numbers (Euclid’s proof). |
| Unit-II | Basic properties of congruence, linear congruences and the Chinese remainder theorem, Fermat’s little theorem, Wilson’s theorem. |
| Unit-III | The sum and number of divisors, the Möbius inversion formula, the greatest integer function, Euler’s phi-function, Euler’s theorem, some properties of the phi-function. |
| Unit-IV | Euler’s criterion, Legendre’s symbol: definition and its properties, evaluation of $(-1\mid p)$ and $(2\mid p)$, Gauss lemma, quadratic reciprocity. |
Reference Books
- Burton David M., Elementary Number Theory, (Seventh Edition) McGraw Hill Education.
- Hardy G. H. and Wright E. M., An Introduction to Theory of Numbers, (Sixth Edition) Oxford University Press.
- Nivan Ivan, Zuckermann H. S. and Montgomery H. L., An Introduction to the Theory of Numbers, (Fifth Edition) John Wiley & Sons Inc.
- Apostol Tom M., Introduction to Analytic Number Theory, Springer.