Question

if n+2 is divisible by 2, is n:
an even number?
an odd number?
or a prime number?

Answer 1

N must be an even number to meet the requirement.

Answer 2

\[\frac{n+2}{2}=integer\]
let k be an integer
Well test what happens if n=2k+1 this would imply n is odd

\[\frac{2k+1+2}{2}\]
We couldn't cancel the 2 on bottom :(

ok so what happens if n=2k this would imply n is even

so we would have

\[\frac{2k+2}{2}=\frac{2(k+1)}{2}=k+1\]

and k+1 is an integer since k is an integer

Answer 3

The expression is divisible for one prime that prime being 2
since
\[\frac{2+2}{2}=\frac{4}{2}=2\]

But this prime is also even while all other primes are odd
(and i'm not saying all odd are prime-lol; i love math)

Answer 4

@artist do you have any questions?

Answer 5

What if our integer that we are looking for is \[\frac{n+2}{2}\]
and that integer could be simplified as \[\frac{n}{2} + \frac{2}{2}\]
Our lovely integer would be \[\frac{n}{2} + 1\]

Since our answer is an integer, n must be an even number so it could be divisible by 2.

Answer 6

if (n+2) is divisible by 2, then (n+2) must be even.
if you take 2 away from ANY even number, you are still left with an even number.
therefore, since (n+2) is even, (n+2-2) must also be even. therefore n is even.

Answer 7

If n is odd so is n+2.
Primes are odd except 2
So n is always even