1. Prove by induction on n that 8n − 3 n is divisible by 5 for any nonnegative integer n 2. Conjecture a formula for the value of 9n mod 10, and prove it correct by induction on n. (Hint: try...

1. Prove by induction on n that 8ⁿ
− 3
ⁿ
is divisible by 5 for any nonnegative integer n

2. Conjecture a formula for the value of 9ⁿ
mod 10, and prove it correct by induction on n. (Hint: try computing 9
ⁿ
mod 10 for a few small values of n to generate your conjecture.)