Reasoning Contest-124

[HELP]

Two mathematicians A and B are given 2 consecutive natural numbers. A does not know the number given to B and vice versa but they know that the numbers are consecutive. (let's say A is given n and B n+1 - so A knows that B's number is either n-1 or n+1 but doesn't know which; same scenario for B) Now they are told that at regular intervals an alarm will sound and they have to conclude whether they know the other guy's number by saying 'Yes' or 'No'. (assume both of them say simulateneously so they cannot change their answer at the last second on hearing the other's reply)

Assuming that both mathematicians are equally intelligent, after how many intervals will one of them say 'Yes' i.e. after how many alarms will one of them guess the other one's number correctly? Also who will guess the correct answer first and why?

There is a perfectly logical solution to this problem even though at first sight it may seem that there is insufficient data.