Question 7
Consider the sequence of perfect square numbers 1, 4, 9, 16, ... . Now, we add 50 to each of the terms and obtain a new sequence 51, 54, 59, 66, ... , after that, we calculate the greatest common divisor (gcd) of each pair of neighboring numbers, for example 51 has 54 as the neighbor so we calculate gcd(51, 54) = 3, 54 has 51 and 59 as the neighbor so we calculate gcd(51, 54) = 3 and gcd(54, 59)=1, and so on. What is the largest possible gcd value that we can get for this sequence?