Mathematical Induction Exploration
Prove the following statements with either induction, strong induction or proof by smallest conterexample.
Prove that 3 | (52n −1) for every integer n ≥ 0.
Prove that 12 +22 +32 +42 + . . . + n2 = [n(n+1)(2n+1)]/6 for every positive integer n.