This is just a funny question that I was elaborating... I know one way to solve (or maybe it's wrong...), but I want know if there is another way to solve this (when we keep adding conditions, there is an possibility of letting the exercise trivial and don't see this, I think...)
The month and day of my birthday are perfect squares and its product is an power of an prime, with positive exponent. Denote by $x$ the square root of the month and $y$ the square root of the day. Then
- If you know the value of the product $xy$, you can certainly deduce the sum $x+y$.
- Knowing the sum $x+y$, even knowing that condition 1 holds, doesn't exists the possibility of deduce the product $xy$.
The sum $x+y$ is relatively prime with the product of the month by the day.
(This isn't my real birthday,
but I accept gifts =p)
Thanks in advance!
And excuse my English...