MATH 406 Study Guide - Midterm Guide: Linear Combination, Euclidean Algorithm

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

Document Summary

Circle your nal answer to each problem if the problem is a computation. Show all your work on these pages, using the backs for scratch paper. No credit will be given for proofs that do not use induction. 5|n5 n: (12 points) show that 3 + 11 is irrational. Math 406: (12 points) using the euclidean algorithm, nd the greatest common divisor of. 330 and 126 and write it as a linear combination of the two numbers: (12 points) find the complete integral solution to. 6x + 9y = 123, and list the non-negative solutions. Math 406: (12 points) find the least positive residue of 535 mod 19, (15 points) solve each of the following if possible: (a) 4x 5(mod 33). (b) 15x 3(mod 21). (c) 18x 12(mod 27). Math 406: (12 points) for any positive integer n, let s(n) be the smallest integer such that n divides s(n)!.