2016 PAMO 3. For any positive integer , we define the integer as
Find the greatest common divisor of the integers .
Hint 1: Let be the greatest common divisor desired. What are the possible primes in ‘s prime factorisation?
Hint 2: Is 2 a divisor of ? How about 4? Can this argument be extended to the other primes that could be in ‘s prime factorisation?