MAS 4214/001 Elementary Number Theory, Fall 2013CRN: 80553Answers, Set 5Qyestion 1.(2 pts)This problem is about solvingax≡b(modm), wherea= 2123 andm= 4632.(a) Use the extended Euclidean Algorithm to findd= gcd(m,a), ands,tso thatd=ms+at.(b) Solve the congruenceax≡b(modm), whenb= 579.(c) Solve the congruenceax≡b(modm), whenb= 379.
Question 2. (2 pts) (Exercise 20.5)Determine whether or not each of the following is true.Give reasonsin each case.(a)x≡3 (mod 7)