show that if p is a prime so that p 3 then p2 1mod12Soluti

show that if p is a prime so that p > 3 then p² = 1(mod12)

Solution

Every prime number p>3can be written in form 6k±1. This is easily proved by considering remainders upon dividing by 6.

p² = (6k±1)²136k²±12k+1112k(3k±1) + 1 12 t +1

p²  = 1 (mod 12)

hence proved   

{ p²=1(mod24) is also right as k(3k±1) is multiple of 2 }