Carry out the following calcula- tions by hand by using the chinese remainder theorem to split each operation into two operations modulo smaller numbers. you must show your work to receive full credit. (a) 23 x 36 mod 55 (b) 29 x 51 mod 91

(c) the diagram shows the first three shapes of a matchsticks arrangement.first shape = 3second shape = 5third shape = 7given m represents the number of matchstick used to arrange the n'th shape.(i) write a formula to represent the relation between m and n. express m as the subjectof the formula.(ii) 19 matchsticks are used to make the p'th shape. find the value of p.