show that every prime number apart from the first two is of the form 6k+1 or 6k-1 using congruences modulo 6

Question

rational · Answer

hint :

$2 \mid (6k +  2)$

$3 \mid (6k + 3)$

$2 \mid (6k +  4)$

anonymous · Answer

still stuck :/

anonymous · Answer

i tried doing rs = (2k+1)(mod 6) and end up reducing down to 6*a+1=rs, where a is in z

rational · Answer

In modulo 6, every integer can be expressed in one of the 6 forms  : `6k, 6k+1, 6k+2, 6k+3, 6k+4, 6k+5`

simply show that four of these forms are always composite

rational · Answer

can an integer expressed in form `6k+2` ever be a prime ?

anonymous · Answer

no, 6k is always even, even + 2 is even

anonymous · Answer

think i have something similar in my notes that ill look at, thanks

rational · Answer

Yes, similarly `6k+3` can never be a prime for $k\ne 0$ because it is always divisible by `3`