Problem of sum & product

[mite]

1. The problem statement, all variables and given/known data
There are two unknown numbers each between 2 & 99 person 'P' is told the product and person 'S' is told the sum when asked about the two numbers their conversation is as follows
P-I dont know them
S-I knew that already
P-Then I know the two numbers
P-Then I know them too
Using these clues we have to find the two numbers



2. Relevant equations
I dont know


3. The attempt at a solution
I have no idea. Can anyone please give me some clue how to solve this.I dont want solution only some clue to solve.

[cheff3r]

okay i got given this question a while back i will start you off, youve got think about all the basic logic parts to adding/multiplying, so i will start you off and then well see weather you can get any further

From p "I do not know the numbers", we can deduce that the product is not the product of two primes. If it were, then Product would have been able to factorize the product into two primes, and would then know the two numbers.

From s "I knew you didn't knew the numbers" we can deduce that the sum must be an odd number, because every even number (at least for small numbers) can be written as the sum of two primes (Goldbach's Conjecture). The only way for S to know that p doesnt know the numbers, is for the sum to be an odd number.