1.1. Let P(n) be the claim that 3 | n(n + 1)(n + 2) for
all integers n1.
P(1) is the statement: 3 | 1.
P(k) is the statement: 3 | k(k + 1)(k + 2), or equivalently, k(k + 1)(k + 2) = 3a for some integer a.
P(k+1) is the statement: 3 | (k + 1)(k + 2) (k + 3), or equivalently, (k + 1)(k + 2)(k + 3) = 3b for some integer b.
For a proof by induction, you first need to check that the statement P(1) is true. Then assume that P(k) is true and use this to show that P(k + 1) is true. It will probably be easier to use the second versions of P(k) and P(k+1) since equations tend to be easier to work with than statements involving the divides symbol.