Mathematical Induction Exploration
Prove the following statements with either induction, strong induction or proof by smallest conterexample.
[size=150]Prove that 3 | (5[sup]2n[/sup] −1) for every integer n ≥ 0.[/size]
[size=150]Prove that 1[sup]2[/sup] +2[sup]2[/sup] +3[sup]2[/sup] +4[sup]2[/sup] + . . . + n[sup]2[/sup] = [n(n+1)(2n+1)]/6 for every positive integer n.[/size]