Ask
your own question, for FREE!
Mathematics
28 Online
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!
n^(3-1) or n^(3)-1?
\[n^3-1\]
because it factors
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
XShawtyX:
Helpud83dude4f All this graphing shi hurts my head like how tf do u do this????
Jasonisyours:
What were the key causes of the French Revolution in 1789?
brianagatica14:
A phone company charges $2 for the first five minutes of a phone call and 30 cents per minute thereafter.
CherryLover:
not sure if ya'll hear of this but last year there was this girl and her name is Aubreigh Wyatt and she was bullied by a group of people and they hated her
ctomk3743:
It's another song I had in mind (please no negative comments) I walk through the rain at night as the wind blows hard and the rain pours down on me.
2 hours ago
1 Reply
1 Medal
2 hours ago
2 Replies
4 Medals
1 hour ago
5 Replies
3 Medals
2 hours ago
41 Replies
3 Medals
1 day ago
8 Replies
7 Medals