MATH 406 Midterm: MATH406_COHEN-J_SUMMER II2011_0101_MID_EXAM

• School: University of Maryland
• Department: Mathematics
• Course: MATH 406
• Professor: All

Document Summary

Put nal answer to each problem in a box if the problem is a computation. Show all your work on these pages, using the backs for scratch paper. The fibonacci numbers {fn} are given by: f0 = 0, f1 = 1 and fn+1 = fn + fn 1 for n 1. 0,1,1,2,3,5,8,13,21,34,55,89,144,233: (20 points) let p1, p2, p3, . , etc. be the set of all primes in order. Prove that pn+1 p1p2p3 pn + 1: (15 points) look at the arithmetic progressions {3n + 1|n = 1, 2, 3, . and. Let p be prime that is in the rst sequence. Prove that it is also in the second sequence. Math 406: (20 points) solve each of the following if possible: (a) 4x 5( mod 33). (b) 15x 6( mod 21). (c) 18x 12( mod 27). Math 406: (20 points) prove by induction that n. 3: (20 points) find the least positive residue of 7357 ( mod 33).