Instructions: (a) you have 3 hours to complete this exam. (b) 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. Phones and devices must be turned o and put away in your bag. Do not keep them in your possession, such as in your pockets. By signing below, you acknowledge that you have ensured that you are complying with the above statement. Please do not write in the table below. Mat 2143 final exam: [3 points] determine all x z such that x 3 (mod 7) and x 2 (mod 8). Solution: we need to nd p, q z such that 7p + 8q = 1. For example p = 1 and q = 1.
