1. (5 points) We know that 3 is a primitive root modulo 31. You can use this without proof. Using that fact, or otherwise, nd all elements of all possible orders modulo 31. Your answers for each order must be given in the residues 15, 14, ...,14, 15. You must explain your reasoning carefully. Hint: There is a (very) painful way to do this and an easy way to do this. We have seen in the proof of the existence of primitive roots how the easy way works