expert level - hard and time consuming

WARNING 1- 如果您一小时内想出一个答案，就不必post了...
WARNING 2- 如果您不会答如下热身题的话， 请不必阅读此题 . see "有趣的逻辑思维测试题 (1)-【8】猜牌问题" - (方块 5)


now 题目如下：





如下...






如下..




如下:



We select two integers from [3,100] and we give their product to Mr.P and
their sum to Mr.S.
Please read their discussion and then find the numbers!


-Mr.P: I can't find the numbers

-Mr.S: Neither can I, but I knew you couldn't

-Mr.P: Now that you said that, I can find them!

-Mr.S: Since you can find then, I can also find them!