Determine two positive integers x and y, with x>y, such that:
- y divides x, and:
- x-y is the harmonic mean of x/y and x*y.
(2(ky*y)*(ky/y))/((ky*y)+(ky/y)) = (ky-y), using the 2-number version of the formula in Wikipedia.
Simplifying nicely to k(y-1)^2 = y^2+1, where 2 is an obvious solution for y if k=5, making x=10.
Then x/y= 10/2 or 5, xy= 10*2=20, x-y=8.
And indeed the harmonic mean of 5 and 20 is 8.
Posted by broll
on 2022-09-15 07:54:04