Mathematics OpenStudy (anonymous):

Show that the the only prime of form n^3-1 is 7. 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.

Latest Questions ejbcb: In Crossroads: A Sad Vaudeville the man sent the woman:
2 hours ago 0 Replies 0 Medals Alyssah1025: What is the converse of the following conditional statement? "If it is sunny, then it is 80u00b0 Fahrenheit.
5 hours ago 0 Replies 0 Medals Alyssah1025: What is the contrapositive of the following statement? "If it does not have four legs, then it is a fish.
5 hours ago 0 Replies 0 Medals Alyssah1025: Jenni wrote a conditional statement and its converse. Conditional: If each angle of a triangle measures 60u00b0, then the sum of the measures of all the ang
5 hours ago 3 Replies 0 Medals kamthekrtr: Thoughts on my song "DND?" https://soundcloud.com/kamtheekrtr/dnd?in=kamtheekrtr/
4 hours ago 3 Replies 0 Medals lifewmylilweeb: Im doing conversions and i need help solving thie problem below step by step' 63
6 hours ago 13 Replies 3 Medals LuvvxTayy: heres a vid of me singing snap(snapping 1,2 where r u?) sorry if i post many of t
3 hours ago 9 Replies 3 Medals Sailor: Help? ;3;
8 hours ago 4 Replies 1 Medal UnknownShadowLove: What are three things you should NEVER do with chemicals in the lab? -Forensic sc
10 hours ago 3 Replies 1 Medal cookie342: Use the periodic table to choose the element that matches each description. halog
9 hours ago 3 Replies 1 Medal