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The Heronian mean $H(a, b)$ is defined as $H(a, b) = \dfrac{a + \sqrt{ab} + b}{3} $. What is the least positive integer $b > 40$ such that $H(10, b)$ is also a positive integer?

 

The Heronian mean H(a,b) is defined as H(a,b)=a+ab+b3. What is the least positive integer b>40 such that H(10,b) is also a positive integer?

 
 Jul 26, 2023
edited by Alan  Jul 27, 2023

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