Oops. We took a Turing machine and dropped it the gears are broken or slipping or something. Instead of moving one unit left, or one unit right. It can now move only l units left or r units right. Prove that if gcd(l,r)=1 then our broken (l,r)-machine is still Turing complete. Discuss how it could kind of still be Turing-complete if l,r were not relatively prime. As a warmup, consider an (2,3)-machine