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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?

 Jun 18, 2021
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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. :)

 

=^._.^=

 Jun 18, 2021

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