anonymous
  • 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?
Discrete Math
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
Do you have any ideas?
anonymous
  • anonymous
not really
anonymous
  • anonymous
Do you know how to start?

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More answers

anonymous
  • 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.
anonymous
  • anonymous
So if I used that approach perhaps I could cancel the 2^.........'s and be left with +1 and -1?
anonymous
  • anonymous
When subtracting
anonymous
  • anonymous
Is that your final answer?
anonymous
  • anonymous
no
anonymous
  • anonymous
do you know how it is done?
anonymous
  • anonymous
Hmm, the number being prime probably has something to do with the problem
anonymous
  • anonymous
idk =\
anonymous
  • anonymous
It does.
anonymous
  • anonymous
But I have no clue how that would play into the solution.
anonymous
  • anonymous
=(
anonymous
  • anonymous
Help me with it? :O
anonymous
  • anonymous
Find out the prime in the would be with the remainder of 0
KingGeorge
  • 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?
anonymous
  • anonymous
Sort of makes sense
anonymous
  • anonymous
how did you get the p and p + 2?
amistre64
  • amistre64
2^n - 1, is prime ... this is given, let it be p 2^n - 1 + 2 = 2^n + 1 = p+2
anonymous
  • anonymous
ah that makes sense
anonymous
  • anonymous
Alright, thanks for the help everyone! I will look over it some more and see if I can get it all making sense.
anonymous
  • anonymous
Ok good luck:)

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