(1 + 3 Points) A 2 (a) Calculate the expression 1 @ 2@...@(n-2) @ (n-1) in the group (Zn,) for (i) n € {3,4,5,6) (ii) n N, n > 2. (b)

Terence Tao's birthday is on July 17th, which is a Monday in 2023. To what days of the week is his/her birthday in 2050 and 2010? Justify the answer in a group-theoretical way. (2 + 2 Points)