(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)