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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?

 Oct 24, 2022
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ab has to be a perfect square.

b has to be a perfect square.

(4 + sqrt(4b) + b)/3 = (4 + 2sqrt(b) + b)/3 = an integer

And from there you just plug values in.

 

9 doesn't work.

16 doesn't work.

25 works.

 

So the value of b that answers this problem is 25.

 Oct 24, 2022

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