Let A be a set of two positive integers and a function `f:A to Z^(+)` is defined as `f(n)=p` , where p is largest prime factor of n.
if the range of f is {3} , then find A. Can A exist uniquely?

Answer

N/a

Explanation

Let A ={n,m} where n and m are positive integers.
`therefore f(n)=f(m)=3`
`implies` Largest prime factor of n and m =3
`implies m=3, m=6, or n=3, m=9 or n=3, m=12, or n=6, m=9,…..`
`implies A={3,6}` or {3,9} or {3,12} or {6,9} , etc.
`therefore ` A cannot be unique.