P6

Part of 2023 Israel National Olympiad

Problems(1)

Set in which each product is a sum

Source: 2023 Israel National Olympiad P6

Determine if there exists a set

S

5783

different real numbers with the following property: For every

a,b\in S

(not necessarily distinct) there are

c\neq d

S

a\cdot b=c+d