1. The problem statement, all variables and given/known data If F is a field than does it imply it must also be a Euclidean domain? 3. The attempt at a solution Yes since for any a,b in F. a=bq for some q in R. In fact let q=(b^-1)a. So the remainder which occurs in a ED is always 0. So the rule for being a ED is satisfied in any field.