Ask
your own question, for FREE!
Mathematics
58 Online
OpenStudy (anonymous):
Show that the the only prime of form n^3-1 is 7.
Still Need Help?
Join the QuestionCove community and study together with friends!
OpenStudy (chaise):
n^(3-1) or n^(3)-1?
OpenStudy (anonymous):
\[n^3-1\]
OpenStudy (anonymous):
because it factors
OpenStudy (anonymous):
n^3-1= n^3-1^3= (n-1)(n^2-n+1) We know: If n is an integer, n-1 is an integer and n^2-n+1 is also an integer. Thus, (n-1)(n^2-n+1)=ab for integers a and b if ab is prime, either a or b must be 1 (or else, we would have more than two factors). Thus, either: n-1=1 OR n^2-n+1=1 If the first is true: n=2 If the second is true, n=0 and n=1 So, we test n=0, n=1, and n=2 in n^3-1 to see which one(s) are prime: n=0, n^3-1=0-1=-1 not prime n=1, n^3-1=1-1=0 not prime n=2, n^3-1=8-1=7 prime Thus, 7 is the only prime in the form of n^3-1.
Can't find your answer?
Make a FREE account and ask your own questions, OR help others and earn volunteer hours!
Join our real-time social learning platform and learn together with your friends!
Join our real-time social learning platform and learn together with your friends!
Latest Questions
notmeta:
I need ideas for a fictional business :P (has to be a sole proprietorship)
4 hours ago
1 Reply
2 Medals
0bviouslyNotRakita:
Letu2019s say you want to go to XYZ Medical School as itu2019s located in Corpus Christi, TX and youu2019d love to live on the beach while attending medical
9 hours ago
0 Replies
0 Medals
Angie2009:
Can anyone here help me learn Korean? My brothers want me to move back to Korea b
9 hours ago
3 Replies
0 Medals
Subshilava:
Which of the following is the real root and which is the non real root X=2+-i X=4
9 hours ago
4 Replies
1 Medal
Alanaaaaaaa:
Shattered Whispers In the dim light where shadows creep, She stood, a specter in my dreams, Eyes like burning coals, secrets to keep, Her laughter danced on
4 hours ago
35 Replies
2 Medals