4

Part of 1990 Balkan MO

Problems(1)

another nice 4-th problem proposed by Romania, not so hard

Source: bmo 1990

Find the least number of elements of a finite set

A

such that there exists a function

f : \left\{1,2,3,\ldots \right\}\rightarrow A

with the property: if

i

j

are positive integers and

i-j

is a prime number, then

f(i)

f(j)

are distinct elements of

A

functioncombinatorics proposedcombinatorics