Prove 5 divides 32^n - 4^n for all n >= 0

[limegreen00]

1. Prove by minimum counterexample that for all n>=0, 5/(3²ⁿ)-4ⁿ)

2. Homework Equations : proof by induction?



3. I tried plugging in 0 for n because that would be the minimum counterexample since 5 can't divide 0. If it's not zero it might be 2 because that works as well. I'm not sure where to go from there or what to state if I am right.

 

[Dick]

I would try to figure out a simpler way to write 3^(2n) mod 5. I.e. what's a simpler expression for its remainder after division by 5. Or just write it as 9^n-4^n and think about factoring.