For all positive integers n, the nth triangular number T_n is defined as T_n = 1+2+3+...+ n$. What is the greatest possible value of the greatest common divisor of 4T_n and n-1?
1 2 1 4 1 2 1 4 1 2 1 4 1 2 1 4 1 2 1 4 1 2 1 4 1 2 1 4 1 2 1 4 1 2 1 4 1 2 1 4 1 2 1 4 1 2 1 4 1 2 1 4 1 2 1 4 1 2 1 4 1 2 1 4 1 2 1 4 1 2 1 4 1 2 1 4 1 2 1 4 1 2 1 4 1 2 1 4 1 2 1 4 1 2 1 4 1 2 1 >> These are the GCD's of [4T_n, n-1] for the first 100 triangular numbers. As you can see, 4 is the greatest GCD.
