Question

5: Prove that only prime number of the form n3 - 1 is 7.
We know that​

Answer 1

Step-by-step explanation:

n3−1 = (n−1)∗(n2+n+1) .Hence it is factorisable.

It is possible if either of (n−1) or (n2+n+1) is equal to 1 and the other one is prime simultaneously.

n−1=1 is n=2 ,then (n2+n+1) = 7 and is prime . So n=2 is a solution.

(n2+n+1)=1 if n=0 or n=-1 ,and both are not natural numbers .

For any n>2 , both n and (n2+n+1) will be greater than 1 ,and hence is composite.