1

Part of 2021 Saudi Arabia IMO TST

Problems(1)

P(T)-a is an odd integer , where p(T) is product of all elements of T

Source: 2021 Saudi Arabia IMO TST p1 (1.2)

For a non-empty set

T

p(T)

the product of all elements of

T

. Does there exist a set

T

2021

elements such that for any

a\in T

P(T)-a

is an odd integer? Consider two cases: 1) All elements of

T

are irrational numbers. 2) At least one element of

T

is a rational number.

irrational numbercombinatoricsodd