Results 1 to 11 of 11

Math Help - Is this a prime number??

  1. #1
    Newbie
    Joined
    Apr 2011
    Posts
    20

    Is this a prime number??

    Is (3^9 -1)/2 prime??I'll also need to justify my answer using the method along the lines of group theory or mod but have no idea :S thxxxxx
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor alexmahone's Avatar
    Joined
    Oct 2008
    Posts
    1,074
    Thanks
    7
    Quote Originally Posted by bryan06 View Post
    Is (3^9 -1)/2 prime??I'll also need to justify my answer using the method along the lines of group theory or mod but have no idea :S thxxxxx
    (3^9-1)/2=[(3^3)3-1^3]/2=(3^3-1)(3^6+3^3+1)/2=[(3^3-1)/2]*(3^6+3^3+1)

    Note that both factors are natural numbers. So, (3^9-1)/2 is not prime.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Apr 2011
    Posts
    20
    thank you so much for your reply, much appreciated~~~but im so sorry i am kind of lost already wen i try to understand (3^9-1)/2=[(3^3)3-1^3]/2...do you actually mean that or is there a typo??or have i mis-read something?the number involved in the question is (3^9 -1)/2 which is 9841, just in case there's any notation error. would you be very kind and explain briefly your working pleaseee?? thankssssss

    Quote Originally Posted by alexmahone View Post
    (3^9-1)/2=[(3^3)3-1^3]/2=(3^3-1)(3^6+3^3+1)/2=[(3^3-1)/2]*(3^6+3^3+1)

    Note that both factors are natural numbers. So, (3^9-1)/2 is not prime.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by bryan06 View Post
    Is (3^9 -1)/2 prime??I'll also need to justify my answer using the method along the lines of group theory or mod but have no idea :S thxxxxx
    No, since it is less than 10000 you need only check for divisibility by odd primes less than 100 and there are only 24 of those and you can rule out 3 and 5 straight off. Now proving it by some other method is another question, maybe the Lucas–Lehmer test would do (but it still looks more complicated than trial division by the primes less than 100)

    CB
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor alexmahone's Avatar
    Joined
    Oct 2008
    Posts
    1,074
    Thanks
    7
    Quote Originally Posted by bryan06 View Post
    thank you so much for your reply, much appreciated~~~but im so sorry i am kind of lost already wen i try to understand (3^9-1)/2=[(3^3)3-1^3]/2...do you actually mean that or is there a typo??or have i mis-read something?the number involved in the question is (3^9 -1)/2 which is 9841, just in case there's any notation error. would you be very kind and explain briefly your working pleaseee?? thankssssss
    I merely factorised the given number (9841=13x757).

    -------------------------------------------------------------

    3^9=(3^3)^3
    1=1^3

    I then used the "difference of cubes" formula.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Apr 2011
    Posts
    20
    ahhhh i see i see thank you soo much

    Quote Originally Posted by alexmahone View Post
    I merely factorised the given number (9841=13x757).

    -------------------------------------------------------------

    3^9=(3^3)^3
    1=1^3

    I then used the "difference of cubes" formula.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Apr 2011
    Posts
    20
    but what happens if we're not allowed a calculator (like in my exam)??becoz then we would never know the number is 9841 and therefore cannot use this method. is there another method possible??perhaps using "mod"?? :S
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor alexmahone's Avatar
    Joined
    Oct 2008
    Posts
    1,074
    Thanks
    7
    Quote Originally Posted by bryan06 View Post
    but what happens if we're not allowed a calculator (like in my exam)??becoz then we would never know the number is 9841 and therefore cannot use this method. is there another method possible??perhaps using "mod"?? :S
    I didn't use a calculator when I wrote post #2...
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Newbie
    Joined
    Apr 2011
    Posts
    20
    so you mean there was no need to know the number was 9841 in the first place??or did u work it out by hand?? cheers

    Quote Originally Posted by alexmahone View Post
    I didn't use a calculator when I wrote post #2...
    Follow Math Help Forum on Facebook and Google+

  10. #10
    MHF Contributor alexmahone's Avatar
    Joined
    Oct 2008
    Posts
    1,074
    Thanks
    7
    Quote Originally Posted by bryan06 View Post
    so you mean there was no need to know the number was 9841 in the first place??
    Exactly.

    Quote Originally Posted by bryan06 View Post
    or did u work it out by hand??
    Nope.
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Newbie
    Joined
    Apr 2011
    Posts
    20
    i get it now thx
    Quote Originally Posted by alexmahone View Post
    Exactly.



    Nope.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: September 24th 2011, 11:23 AM
  2. Replies: 1
    Last Post: September 2nd 2009, 08:31 AM
  3. Is it a prime number ??
    Posted in the Algebra Forum
    Replies: 4
    Last Post: April 29th 2009, 06:07 AM
  4. prime number
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: September 23rd 2008, 05:02 PM
  5. Number theory, prime number
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: September 17th 2006, 08:11 PM

Search Tags


/mathhelpforum @mathhelpforum