MATC15H3 Final: MATC15H Final Exam Winter 2014
Document Summary
Do not open this booklet until instructed to do so. Notes: there are 12 numbered pages in the quiz. It is your responsibility to ensure that, at the start of the exam, this booklet has all its pages: no calculators allowed, justify your answers, justify your answers. Matc15h: [14 marks] page 1 (a) suppose that a, b, c are integers. Describe (without proof) the general solution in integers x, y of the equation ax + by = c. Matc15h: [18 marks] (a) de ne multiplicative arithmetic function". page 3 (b) let f and g be arithmetic functions and de ne h(n) for all n 1 by h(n) = x d|n f (d)g (cid:16) n d(cid:17) . Show that, if f and g are multiplicative, then so is h. Question 2(b) continued (if space needed) (c) give an example where f and g are totally multiplicative but h is not.
