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The Heronian mean H(a, b) is defined as H(a, b) = (a + sqrt(ab) + b)/3. What is the least positive integer b > 4 such that H(4,b) is also a positive integer? 

 Jul 8, 2022
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H(4, b) = (4 + 2sqrt(b) + b)/3.

In order for this to be a postive integer b has to be a perfect square and the numberator has to be divisble by 3. The smallest perfect square that outputs a postive integer is b = 25. 

 Jul 8, 2022

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