Question

(b) Given that p = 6n + 1, show that p2 + 2 is divisible by 3.

Answer 1

See below.

Explanation:

p^2 + 2

= (6n + 1)^2 + 2

= 36n^2 + 12n + 1 + 2

= 36n^3 + 12n + 3

= 3(12n^2 + 4n + 1).

- which is divisible by 3.