I would like to know of the line of approach one needs to take in the following (and similar problems involving elementary concepts of GCD of numbers)problem.
The problem is-
For any 2 integers a,b, prove that the (a+b,a-b)>=(a,b)
where (x,y) represents the GCD of the numbers x,y.
Considering the reply, i am now forced to ask this question-
Can you prove the statement "Any common divisor of a and b is a divisor of a+b and a-b", because at face value, it seems to be quite logical.
But is there a mathematical treatment this statement can be given?