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

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- April 25th 2011, 06:10 AMbryan06Is 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

- April 25th 2011, 06:15 AMalexmahone
- April 25th 2011, 09:03 AMbryan06
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

- April 25th 2011, 09:03 AMCaptainBlack
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 - April 25th 2011, 09:11 AMalexmahone
- April 25th 2011, 09:14 AMbryan06
- April 25th 2011, 09:18 AMbryan06
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

- April 25th 2011, 09:20 AMalexmahone
- April 25th 2011, 10:17 AMbryan06
- April 25th 2011, 10:19 AMalexmahone
- April 25th 2011, 10:24 AMbryan06