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
Question 5 and 6.
(5) (4 pts) Show the following result: if m = nd is a positive composite number (i.e., n > 1 and d > 1), then N 2m-1 is not a prune number Hint. Recall the finite geometric series: if r is any number, then Eratosthenes of Cyrene (с. 276 BC-e 195/194 BC) was a Greek mathematician. geographer, poet, astrononer, and music theorist. He was a man of learning, becoming the chief librarian at the Library of Alexandria. He invented the discipline of geography, including the terminology used today. (Source: Wikipedia) 1++12 +1 Use this formula (which you dont have to prove here) and plug in a suitable value for z so as to conclude that 2m is not prime. Remark. This shows that the number N -2m-1 can only be a prime if m itself is prime. Primes of the form 2-1, where p is a prime, are called Mersenne primes. For p-2,3,5,7 the number 2-1 s indeed prime, but 2--2047-23 89 is composite. In the past, the largest known prime (found using computers) has often been a Mersenne prime, but it is not known whether there are infinitely many Mersenne primes (6) (2 pts each) Linear Diophantine Equations. Let a,b,c E Z and suppose a 0 b. It has been shown in class that the linear Diophantine equation az +by-c has an integral solution if (a, b)-1, and given a particular integral solution (ro, Vo) we have found a formula which describes all other integral solutions (x, y),namely a-o + kb and y -yo-ka, where k can be any integer In this problem you are asked to find all positive integral solutions (a, y), that is: 0 and y>0. In order to do so, find first some solution (ro. yo) (which is possibly not positive), and then determine the positive solutions using the formulas above (1) Find an integral solutions (ro. yo)of 35y-27. Then find al positive integral solutions to this equation. (ii) Find an integral solutions (ro, yo) of 715y-51. Then find all positive integral solutions to this equation (ii) Find all positive integral solutions (, y, 2) of 3r 5y +7: 31
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.