MATH 323 Midterm: Math 323 exam2-323-05

• School: University of Arizona
• Department: Mathematics Main
• Course: MATH 323
• Professor: All

Document Summary

Exam # 2 friday july 29, 2005. Partial credit is possible, but you must show all work. All you need to do is four problems. I hereby testify that this is individual work. Signed: (a) for what values of n in the eld z7 is 3n. 2 + 2n 5 = 0? (b) solve in the eld z7 the equation n! 2: (a) find the multiplicative inverse of 18 in the eld z41 (note that 41 is a prime number). (b) find all the x and y in z for which. 18x + 41y = 1: let a > 1 be a given xed real number. De ne the sequence (xn)n n by: x1 = 1 and xn+1 = a + xn. 3 (a) show that (xn)n n is a monotone increasing sequence. (b) show that for all n n , a < xn < 2a. (c) deduce that (xn)n n is convergent.