4. (4 points) (a) Use that 52|1 1 = (52" 1)(52" + 1) to prove that 52 factors 2. - 1 contains exactly n +2 (b) Conclude from (a) that the order of 5 in (Z/2"Z)* equals 2n-2 (for n > 2). (C) Show that for n > 2 the map a mod 2Ha mod 4 is a well defined surjective ho- momorphism from (Z/2"Z)" to (Z/4Z)", and its kernel is the subgroup generated by 5. (d) Determine the number of elements of order 2). (C) Show that for n > 2 the map a mod 2Ha mod 4 is a well defined surjective ho- momorphism from (Z/2"Z)" to (Z/4Z)", and its kernel is the subgroup generated by 5. (d) Determine the number of elements of order