MT1sum211_mk

# MT1sum211_mk - (unless noted otherwise(7 Be careful to...

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MAT 312/AMS 351 Midterm I (Make-up exam). August 3, 2011 10:00-11:30am Name: ID: DO NOT OPEN THIS EXAM YET (1) Fill in your name and Stony Brook ID number. (2) This exam is closed-book and closed-notes; no calculators, no phones. (3) Please write legibly to receive credit. Circle or box your ﬁnal answers. If your solution to a problem does not ﬁt on the page on which the problem is stated, please indicate on that page where in the exam to ﬁnd (the rest of) your solution. (4) You may continue your solutions on additional sheets of paper pro- vided by the proctor. If you do so, please write your name and ID number at the top of each of them and staple them to the back of the exam (stapler available); otherwise, these sheets may get lost. (5) Anything handed in will be graded; incorrect statements will be pe- nalized even if they are in addition to complete and correct solutions. If you do not want something graded, please erase it or cross it out. (6) Show your work; correct answers only will receive only partial credit

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Unformatted text preview: (unless noted otherwise). (7) Be careful to avoid making grievous errors that are subject to heavy penalties. (8) If you need more blank paper, ask a proctor. Out of fairness to others, please stop working and close the exam as soon as the time is called. A signiﬁcant number of points will be taken oﬀ your exam score if you continue working after the time is called. You will be given a two-minute warning before the end. 1 2 3 4a 4b 4c 5 Total 1 1. (15 points) Find the prime decomposition of the number 1! · 2! · 3! · 4! · 5! · 6! 2. (20 points) Compute 19 37 mod 12. 2 3. (10 points) Find the maximal power of 5 that divides 100! 4. a) (15 points) Solve the congruence 28 x = 7 mod 63. 3 b) (20 points) Solve the system of congruences x = 7 mod 10 , x = 13 mod 19 . c) (10 points) Find the greatest common divisor of 313 and 515. Justify your answer. 4 5. (10 points) Prove the identity 1 · 2 · 3 + 2 · 3 · 4 + ... + n · ( n + 1) · ( n + 2) = n ( n + 1)( n + 2)( n + 3) 4 . 5...
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MT1sum211_mk - (unless noted otherwise(7 Be careful to...

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