[The title of the thread is intentionally ungrammatical; it's based on a classic RHP thread from many years ago.]

There are two positive integers: n1, and n2. Both are greater than 1, but less than 100.

Mr. Product knows the product of the two numbers. Mr. Sum knows the sum of the two numbers.

They have a conversation:

Mr P: I know the product of n1 and n2, but I don't know either number.

Mr S: I know their sum, and I knew you did not know either n1 or n2.

Mr P: Interesting. Armed with that information, I now know the values of n1 and n2.

Mr S: Given what you have just said, I also now know the values of n1 and n2.

[I need not add that both gentlemen are math whizzes and impeccable logicians.]

The two men found the values of the two numbers during their short conversation. Can you?

There are two positive integers: n1, and n2. Both are greater than 1, but less than 100.

Mr. Product knows the product of the two numbers. Mr. Sum knows the sum of the two numbers.

They have a conversation:

Mr P: I know the product of n1 and n2, but I don't know either number.

Mr S: I know their sum, and I knew you did not know either n1 or n2.

Mr P: Interesting. Armed with that information, I now know the values of n1 and n2.

Mr S: Given what you have just said, I also now know the values of n1 and n2.

[I need not add that both gentlemen are math whizzes and impeccable logicians.]

The two men found the values of the two numbers during their short conversation. Can you?