a. Use mathematical induction to prove that for any positive
integer ?, 3 divide ?^3 + 2?
(leaving no remainder).
Hint: you may want to use the formula: (? + ?)^3= ?^3 + 3?^2 * b +
3??^2 + ?^3.
b. Use strong induction to prove that any positive integer ? (? ≥
2) can be written as a
product of primes.