- #1

Math100

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- 207

- Homework Statement
- Prove the assertion below:

The only prime of the form n^2-4 is 5.

- Relevant Equations
- None.

Proof: Suppose p is a prime such that p=n^2-4.

Then we have p=n^2-4=(n+2)(n-2).

Note that prime number is a number that has only two factors,

1 and the number itself.

Since n+2>1 for ##\forall n \in \mathbb{N}##,

it follows that n-2=1, and so n=1+2=3.

Thus p=n^2-4=3^2-4

=9-4

=5.

Therefore, the only prime of the form n^2-4 is 5.

Above is my proof for this assertion. Can anyone please verify/review it and see if it's correct?

Then we have p=n^2-4=(n+2)(n-2).

Note that prime number is a number that has only two factors,

1 and the number itself.

Since n+2>1 for ##\forall n \in \mathbb{N}##,

it follows that n-2=1, and so n=1+2=3.

Thus p=n^2-4=3^2-4

=9-4

=5.

Therefore, the only prime of the form n^2-4 is 5.

Above is my proof for this assertion. Can anyone please verify/review it and see if it's correct?