i did something similar, problem is I don’t think you can assume w_2k and u_2k are still divisible by 11 when proving for the case of n=k+1, since you are only assuming that there is an implication between the 2. doing it the way you did means the original statement 11| w2n => 11|u2n is only necessarily true if w2, w4 … w2n are all divisible by 11 as well.Here's my attempt. I've probably over-complicated it or am just plain wrong:
Base case () – Trivial
Inductive hypothesis – Assume true for some non-negative integer :
Inductive step – RTP true for :