Zookal
Zookal

We’d love to hear any feedback or comment from you!

© 2011-2021 Zookal Pty Ltd

View question and answer

From our collection of questions and answers
Other · Other
Question details
1-4
1. Let k, m, n Z be nonzero integers. a) (5 pt) Show that ged(m, n) is a linear combination of m and n (that is, show that if d- ged(m, n) then there are integers a and b such that am + bn d). b) (3 pt) Show that if gcd(k, m) = 1 and gcd(k, n) = 1, then gcd(k, mm) = 1. c) (3 pt) Show that if gcd(k, m) = 1 and k divides mn, then k divides n. 2. (5 pt) Let m, n E Z be nonzero integers, d gcd(m, n) and L = lcm(m, n). Show that dL = man. 3. Let n E N be a natural number, and consider Z, the integers modulo n (this is the set of equivalence classes modulo the equivalence relation ~where mim2 if and only if n|(mi -m2). a) (3 pts) We define the set U(Zn) (lalgcd(a, n) - 1. Show that if [a e U(2n) and z E [a] then gcd(x, n) = 1. b) (3 pts) Show that if [a], [b E U(Zn) then (ab E U(Zn). c) (5 pts) Show if [al E U(Z) then a [1 for some m E N d) (G, 5pts) Show that if n pP2P with each p, prime and each a, E N then IU(Zm)- 4. (5 pts) (Chinese Remainder Theorem) Suppose that if ni,n2, nk İs a collection of pairwise relatively prime positive integers and let N = nin2 …nk. Show that the systern of congruences r a mod(n) has a unique solution z such that 0 s : s N-1 (recall that a divisible by n) amod(n) means that (r - a) is
Answer
Find step-by-step answers from expert tutors to questions asked by students like you. Start 14-day free trial.Find step-by-step answers from expert tutors to questions asked by students like you. Start 14-day free trial.Find step-by-step answers from expert tutors to questions asked by students like you. Start 14-day free trial.Find step-by-step answers from expert tutors to questions asked by students like you. Start 14-day free trial.Find step-by-step answers from expert tutors to questions asked by students like you. Start 14-day free trial.Find step-by-step answers from expert tutors to questions asked by students like you. Start 14-day free trial.Find step-by-step answers from expert tutors to questions asked by students like you. Start 14-day free trial.Find step-by-step answers from expert tutors to questions asked by students like you. Start 14-day free trial.Find step-by-step answers from expert tutors to questions asked by students like you. Start 14-day free trial.Find step-by-step answers from expert tutors to questions asked by students like you. Start 14-day free trial.Find step-by-step answers from expert tutors to questions asked by students like you. Start 14-day free trial.Find step-by-step answers from expert tutors to questions asked by students like you. Start 14-day free trial.Find step-by-step answers from expert tutors to questions asked by students like you. Start 14-day free trial.Find step-by-step answers from expert tutors to questions asked by students like you. Start 14-day free trial.

Find step-by-step answers from expert tutors to questions asked by students like you. Start 14-day free trial.Find step-by-step answers from expert tutors to questions asked by students like you. Start 14-day free trial.Find step-by-step answers from expert tutors to questions asked by students like you. Start 14-day free trial.Find step-by-step answers from expert tutors to questions asked by students like you. Start 14-day free trial.Find step-by-step answers from expert tutors to questions asked by students like you. Start 14-day free trial.Find step-by-step answers from expert tutors to questions asked by students like you. Start 14-day free trial.Find step-by-step answers from expert tutors to questions asked by students like you. Start 14-day free trial.Find step-by-step answers from expert tutors to questions asked by students like you. Start 14-day free trial.Find step-by-step answers from expert tutors to questions asked by students like you. Start 14-day free trial.Find step-by-step answers from expert tutors to questions asked by students like you. Start 14-day free trial.Find step-by-step answers from expert tutors to questions asked by students like you. Start 14-day free trial.Find step-by-step answers from expert tutors to questions asked by students like you. Start 14-day free trial.Find step-by-step answers from expert tutors to questions asked by students like you. Start 14-day free trial.Find step-by-step answers from expert tutors to questions asked by students like you. Start 14-day free trial.