Algebraic Methods

a.

Prove that the following statement is not true.

$m\,$ is an odd number greater than 1 $⇒m2+4\Rightarrow m^2 + 4$ is prime.

[2]

b.

By considering separately the case when $n\,$ is odd and the case when $n\,$ is even, prove that the following statement is true.

$n\,$ is a positive integer $⇒n2+1\Rightarrow n^2 + 1$ is not a multiple of 4.

[4]

a.

Prove that the following statement is not true.

$m\,$ is an odd number greater than 1 $⇒m2+4\Rightarrow m^2 + 4$ is prime.

[2]

b.

By considering separately the case when $n\,$ is odd and the case when $n\,$ is even, prove that the following statement is true.

$n\,$ is a positive integer $⇒n2+1\Rightarrow n^2 + 1$ is not a multiple of 4.

[4]

Algebraic Methods Questions