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Let f(x)=12x+7 and g(x) = 5x+2 whenever x is a positive integer. Define h(x) to be the greatest common divisor of f(x) and g(x). What is the sum of all possible values of h(x)?

 Jul 28, 2020
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Let f(x)=12x+7 and g(x) = 5x+2 whenever x is a positive integer. Define h(x) to be the greatest common divisor of f(x) and g(x). What is the sum of all possible values of h(x)?

 

The gcd of f(x) and g(x) when x is a positive integer, is 1 for most values of x and 11 when x is 4, 15, 26, ...etc.

 

So the sum is 12.

 Jul 28, 2020

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