text: 1) show that if p >=5 is a prime number, then p^2 + 2 is composite (hint: p takes one of the forms 6k+1 or 6k 1) show that if p >=5 is a prime number, then p^2 + 2 is composite (hint: p takes one of the forms 6k+1 or 6k + 5 (why?)) well, p can take only 6k+1 or 6k+5 because  6k is divisible by 6 6k+1 ok 6k+2 is divisible by 2 6k+3 is divisible by 3 6k+4 is divisible by 2 6k+5 ok  and then after that it goes back to 6k.  case 1 : p = (6k+1)^2 + 2 = 36k^2+12k+3 can be factored into 3(12k^2+4k+1), therefore divisible by 3, and not prime  case 2 : p = (6k+5)^2 + 2 = 36k^2 + 60k + 27  also divisible by 3 for the same reason as case 1.