Hey all, some help finishing this proof would be appreciated:
For all k in the Naturals, k^3 + 5k is divisible by 6.
1^3 + 5(1) = 6 which is divisible by 6
P(n): n^3 +5n = 6y
(n+1)^3 + 5(n+1) = 6z
(n^3 + 3n^2 + 3n + 1) + 5(n+1)
6y + 3n^2 + 3n + 6 = 6z
3(2y + n^2 + n + 2) = (3*2)z
where do we go from here? How can I show divisibility by 6 here? Thanks in advance for the help!