MAT 2143 Final: MAT2143 Final Exam 2016
Document Summary
Instructions: (a) you have 80 minutes to complete this exam. (b) the number of points available for each question is indicated in square brackets. (c) all work to be considered for grading should be written in the space provided. The reverse side of pages is for scrap work. If you nd that you need extra space in order to answer a particular question, you should continue on the reverse side of the page and indicate this clearly. Please do not write in the table below. Mat 2143 midterm exam: (a) [2 points] write down the de nition of a prime number. Solution: suppose that d > 0 and d|k2 + 1 and d|k2 2. Then d|(k2 + 1) (k2 2) = 3 d = 1 or d = 3. Next we show that d = 3 is impossible. To this end, we show that 3 does not divide k2 + 1.
