MathDB

Set 2
2.1 What is the last digit of

2022 + 2022^{2022} + 2022^{(2022^{2022})}

?
2.2 Let

T

be the answer to the previous problem. CMIMC executive members are trying to arrange desks for CMWMC. If they arrange the desks into rows of

5

desks, they end up with

1

left over. If they instead arrange the desks into rows of

7

desks, they also end up with

1

left over. If they instead arrange the desks into rows of

11

desks, they end up with

T

left over. What is the smallest possible (non-negative) number of desks they could have?
2.3 Let

T

be the answer to the previous problem. Compute the largest value of

k

such that

11^k

divides

T! = T(T - 1)(T - 2)...(2)(1).

PS. You should use hide for answers.

Problem Statement