Question

Show that if p and p + 2 with p ≥ 5, are both primes then
the number p + 1 is always divisible by 6.

Answer 1

p and p+2 are surely odd,, thus p+1 is even --> hence p+1 is always divisible by 2.
we now need to prove p+1 is also divisible by 3..am stuck there..

Answer 2

p + 1 is even right?

Answer 3

yep..

Answer 4

hmn wait

Answer 5

yes..maybe even i made a breakthrough,,i shall just post something..

Answer 6

p is either equivalent to 1 mod 3 or 2 mod 3.
then p+2 is the other one.
So p+1 must be 0 mod 3

Answer 7

exactly what i was going to post.. :D

Answer 8

thank you buddies :)

Answer 9

:) welcome though I didn't help

Answer 10

well you gave my question time..thats not a small thing! ;)

Answer 11

You made me feel proud haha