Question

Can yu prove using the method of mathematical induction that x^2 - 1 is divisible by 3 for all positive integers x that are not divisible by 3?

Answer 1

x^2-1 =(x+1)(x-1) so, x^2 -1 divisible by 3 if either of (x+1) or (x-1) divisible by 3

Answer 2

if x+1 divisible by 3, then x = -1 mod3 that means x is not divisible by 3
and x =-1 = 2 (mod 3)

Answer 3

do the same with x -1