- #1

Math100

- 793

- 220

- Homework Statement
- Prove the assertion below:

Any prime of the form 3n+1 is also of the form 6m+1.

- Relevant Equations
- None.

Proof: Suppose that any prime of the form 3n+1

is also of the form 6m+1.

Note that 2 is the only even prime number

and it is not of the form 3n+1.

This means any prime of the form 3n+1 must be odd.

Since 3n+1 is odd, it follows that 3n must be even.

Then we have n=2m for some integer m.

Thus 3n+1=3(2m)+1

=6m+1.

Therefore, any prime of the form 3n+1 is also of the form 6m+1.

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

is also of the form 6m+1.

Note that 2 is the only even prime number

and it is not of the form 3n+1.

This means any prime of the form 3n+1 must be odd.

Since 3n+1 is odd, it follows that 3n must be even.

Then we have n=2m for some integer m.

Thus 3n+1=3(2m)+1

=6m+1.

Therefore, any prime of the form 3n+1 is also of the form 6m+1.

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