Prove results involving integers, e.g. proving that the product of two consecutive odd numbers is an odd number and 5𝑛2 + 3𝑛 + 6 ∀𝑛 ∈ ℤ is an even number.

Use the table provided to prove that for any integer n, the expression 7n² + 5n is always even.

Prove that the product of any two consecutive even integers is divisible by 8.

Prove that the expression 3n² + 5n + 8 is an even number for all n ∈ ℤ.