Discrete mathematics: Prove by any method: If n is an integer then n2 +3n+1 is odd ? Prove by mathematical induction the following statement: n3 +11n is divisible by 3 for ∀n≥1. Find the general term...

Discrete mathematics:

Prove by any method: If n is an integer then n2 +3n+1 is odd ?

Prove by mathematical induction the following statement:
n3 +11n is divisible by 3 for ∀n≥1.

Find the general term of the recurrence relation:
x1=1 and x2=2, xn=2xn−1+3xn−2, ∀ n≥3.