Let v be a Euclidean norm on a Euclidean domain D. 

a. Show that if s ∈ Z such that s + v(1) > 0, then η : D^* → Z defined by η(a) = v(a) + s for nonzero a ∈ D is a Euclidean norm on D. As usual, D^* is the set of nonzero elements of D. 

b. Show that for t ∈ Z⁺, λ : D* → Z given by λ(a) = t · v(a) for nonzero a ∈ D is a Euclidean norm on D. 

c. Show that there exists a Euclidean norm µ, on D such that µ,(1) = 1 and µ(a) > 100 for all nonzero nonunits a ∈ D.