Question

Determine all primes of the form n 3 − 1.​

Answer 1

Answer:

Correct option is

A

2

In mathematics, a Mersenne prime is a prime number of the form 2

n

−1. This is to say that it is a prime number which is one less than a power of two. The first four Mersenne primes are 3,7,31,127 .

Here, Given that n

3

−1,n=2

So, prime number =2

3

−1

Answer 2

Answer:

I'll explain it in two ways.

{1.}

When we factorize n^3−1,

We get (n−1)(n^2+n+1)

You might be wondering

If we choose an odd number to be n, it will clearly give an even number as result, which is not prime.

Taking the very first even number, we get n = 2, and hence,

(n−1)(n2+n+1)=1.7=7

Which is prime.

Any integer greater than 2 gives n-1>1, which in turn is composite.

But I guess n2+n+1

Yields a good number of primes.

{2.}

n^3−1=(n−1)(n^2+n+1)

when n = 1

n^3−1=0

when n = 2

n^3=7

7=(2−1)(2^2+2+1)

For n = 2

n^3−1 is a product of two integers. 1 and 7.

For any other value of positive integer n, n^3−1 will be a product of two integers, both of which will be greater than 1. Thus it will be a composite number. Hence the only prime of the form n3−1 is 7.

Step-by-step explanation:

Hope that helps!