MATC15H3 Final: MATC15H Final Exam Winter 2011
Document Summary
Do not open this booklet until instructed to do so. Notes: there are 9 numbered pages in the quiz. It is your responsibility to ensure that, at the start of the exam and at the end of the exam, this booklet has all its pages: no calculators allowed, justify your answers. Matc15h page 1: [16 marks] state the fundamental theorem of arithmetic and use it to prove there are in nitely many primes. Matc15h page 2: [16 marks] using the euclidean algorithm nd all solutions of. Matc15h: [17 marks] (a) de ne multiplicative function". page 3 (b) for which positive integers n is the following function odd, (n, (n, (n) Matc15h page 5: [16 marks] state and prove euler"s generalization of fermat"s theo- rem. Matc15h: [17 marks] (a) de ne quadratic residues and non residues. page 6 (b) de ne primitive root.
