Mediterranian mathematics competition 2005, problem 1
Source: Mediterranian Mathematics Competition 2005, Problem 1
January 11, 2006
combinatorics proposedcombinatorics
Problem Statement
The professor tells Peter the product of two positive integers and Sam their sum. At first, nobody of them knows the number of the other.
One of them says: You can't possibly guess my number.
Then the other says: You are wrong, the number is 136.
Which number did the professor tell them respectively? Give reasons for your claim.