"Find all positive integers n s.t. n, n+4, n+8 are prime." (Write everything out; I need this for math tournament)

[MareX]

Determine all positive integers n, for which n, n+4 and n+8 are prime numbers.
If someone could writte me everything about this since im going on math tournament i need to know all steps to writte for this, thanks in advance

 

[pka]

Determine all positive integers n, for which n, n+4 and n+8 are prime numbers. If someone could writte me everything about this since im going on math tournament i need to know all steps to writte for this.

From the instructions we know that the \(\displaystyle n's\) are prime numbers. So start with \(\displaystyle n=2\).
Then try \(\displaystyle n=3\). So-on.

 

[topsquark]

If someone could writte me everything about this...

Don't you think learning how to do it would be much better than just getting it for you?

"Write me everything about this." That's a pretty monumental task you are asking for. Let's pare this down a bit. What have you been able to do with it?

-Dan

 

[FriendlyAsian]

Suppose that n is not 3, then the remainder when we divide n by 3 is 1 or 2. Since n, n+4 and n+8 are prime numbers, none of those can be divisible by 3, which is impossible as the three numbers have different remainders when divided by 3. Hence, n must be 3.

 

[Harry_the_cat]

@MareX
You say "Write everything out; I need this for a math tournament".
Just a question of honesty. How would you feel if you won this tournament on the basis of someone else's work? Would you accept the prize and the glory?
Isn't that cheating??