MathDB

Consider the set

I=\{ 1,2, \cdots, 2020 \}

. Let

W= \{w(a,b)=(a+b)+ab | a,b \in I \} \cap I

Y=\{y(a,b)=(a+b) \cdot ab | a,b \in I \} \cap I

be its two subsets. Further, let

X= W \cap Y

.
(1) Find the sum of maximal and minimal elements in

X

. (2) An element

n=y(a,b) (a \le b)

Y

is called excellent, if its representation is not unique (for instance,

20=y(1,5)=y(2,3)

). Find the number of excellent elements in

Y

.
(2) is only for Grade 11.

Problem Statement