Tutorial sheets :

Tutorial 1  Euclidean Algorithm (Bezout's Theorem), GCD and LCM, Complexity of Euclidean Algorithm

Tutorial 2 Fundamental Theorem of Arithmetic, Primes of the form 4k-1, Congruence equations I : Chinese Remainder Theorem 

Tutorial 3 Complete and Reduced Residue Systems, Congruence equations II : Hensel's Lemma, Euler Phi Function (Remarks on Hensel's Lemma)

Tutorial 4 Orders of an element, Order minimality lemma, Primitive roots : What, How 1 How 2, How many and When

Reading week [Practice 1 Q2] [Practice 3 Q8] [Practice 1 Q8] 

Tutorial 5 Quadratic residues and non-residues, Euler's criterion and applications, Intro to Legendre symbols

Tutorial 6 Quadratic reciprocity and its applications (i) Find all p such that (a/p)=1, (ii) Primitive roots (iii) Quadratic congruences

Tutorial 7 Advanced questions on Primitive roots, Quadratic residues and reciprocity 

Tutorial 8 Sum of two squares theorem, Aside : sum of three squares, Algebraicity and rationality of numbers

Tutorial 9 Liouville's theorem : transcendental numbers,  Rational root theorem, Strategies towards Diophantine equations I : Quadratics

Tutorial 10 (Substituted by Dominik Bullach) Pythagoras triples and applications, Strategies towards Diophantine equations 

Page for 2017 Spring : Elementary Number Theory (the previous version of this course)