MAT-3110 Midterm: MATH 3110 App State Fall2006 Exam1
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Use the backs of the exam pages for scratchwork or for continuation of your answers, if necessary. Then justify your choice! (a) let a, b, u, and v be integers such that au + bv = 2. True / possible / false: the greatest common divisor of a and b is 2. True / possible / false: the equation 2x y mod 999 has a solution x z. (c) let n be a positive integer. True / possible / false: both cancellation laws hold in zn. (d) let f be a eld. True / possible / false: f (x) is irreducible. 4: (10 points): basics (a) let r be a ring with 1. Prove one of the following: let r be a ring where a2 = a for each a r. show that r is commutative. Hint: for all a, b r, (a + b)2 = (a + b) and (a + a)2 = (a + a).
