As n ranges over the positive integers, what is the sum of all possible values of the greatest common divisor of 3n + 4 and n + 18?
By the euclidean theorum.
gcd(3n + 4, n + 18)
gcd(2n - 14, n + 18)
gcd(n - 32, n + 18)
gcd(n - 32, 50)
The factors of 50 are 1, 2, 5, 10, 25, 50.
So the sum is 1 + 2 + 5 + 10 + 25 + 50 = 93
Hopefully that's right. :)
=^._.^=
