Uhm in Q1, letting k be even and k be odd ie k=2p and k=2p+1 works just fine. Not sure the fuss with 4...but this comes from this number theory concept called modulo arithmetic that claims that every integer k can be written as either 4p, 4p+1, 4p+2, 4p+3, because when you reach 4p+4 you looped...