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