OpenStudy (anonymous):

Need help with a discrete math problem. Contriutor to the Great Internet Mersenne Prime Search, Curtix Cooper, of the Iniversity of Central Missouri, recently discovered that 2^57,885,161 - 1 is prime. To date, no larger number has been shown to be prime. What is the greatest common divisor of 2^57,885,161 - 1 and 2^57,885,161 + 1?

4 years ago
OpenStudy (anonymous):

Do you have any ideas?

4 years ago
OpenStudy (anonymous):

not really

4 years ago
OpenStudy (anonymous):

Do you know how to start?

4 years ago
OpenStudy (anonymous):

Well I know how to find the gcd of smaller numbers like 16 and 27 by dividing the larger number by the smaller number. Then I take the remainder and divide the smaller number by the remainder and continue that process until the remainder is 0. That leaves me with the answer. But with a number this big that process would take very long. So I'm not really sure how to start.

4 years ago
OpenStudy (anonymous):

So if I used that approach perhaps I could cancel the 2^.........'s and be left with +1 and -1?

4 years ago
OpenStudy (anonymous):

When subtracting

4 years ago
OpenStudy (anonymous):

Is that your final answer?

4 years ago
OpenStudy (anonymous):

no

4 years ago
OpenStudy (anonymous):

do you know how it is done?

4 years ago
OpenStudy (anonymous):

Hmm, the number being prime probably has something to do with the problem

4 years ago
OpenStudy (anonymous):

idk =\

4 years ago
OpenStudy (anonymous):

It does.

4 years ago
OpenStudy (anonymous):

But I have no clue how that would play into the solution.

4 years ago
OpenStudy (anonymous):

=(

4 years ago
OpenStudy (anonymous):

Help me with it? :O

4 years ago
OpenStudy (anonymous):

Find out the prime in the would be with the remainder of 0

4 years ago
OpenStudy (kinggeorge):

Well, let \(2^{57,885,161}-1=p\). Then you're asked to find the gcd of \(p\) and \(p+2\). Since both \(p\) and 2 are prime, any common divisor greater than 1 must divide both \(p\) and 2. Does this make sense, and can you finish it from here?

4 years ago
OpenStudy (anonymous):

Sort of makes sense

4 years ago
OpenStudy (anonymous):

how did you get the p and p + 2?

4 years ago
OpenStudy (amistre64):

2^n - 1, is prime ... this is given, let it be p 2^n - 1 + 2 = 2^n + 1 = p+2

4 years ago
OpenStudy (anonymous):

ah that makes sense

4 years ago
OpenStudy (anonymous):

Alright, thanks for the help everyone! I will look over it some more and see if I can get it all making sense.

4 years ago
OpenStudy (anonymous):

Ok good luck:)

4 years ago