10 marks When introducing Euclid's algorithm in class, I made use of the following claim: Let d, u and v be positive integers. We have du and dlu if and only if dv and dl (u mod v) Now prove this claim Hint: Make sure to prove both the "if" and "only if in this claim. The following identity mentioned in class is useful: u mod u = u-ulu/u 10 marks When introducing Euclid's algorithm in class, I made use of the following claim: Let d, u and v be positive integers. We have du and dlu if and only if dv and dl (u mod v) Now prove this claim Hint: Make sure to prove both the "if" and "only if in this claim. The following identity mentioned in class is useful: u mod u = u-ulu/u