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Harmonic Harmony 3 (Posted on 2022-09-15) Difficulty: 3 of 5
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.

No Solution Yet Submitted by K Sengupta    
Rating: 4.5000 (2 votes)

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computer solution Comment 3 of 3 |
clearvars,clc
for x=1:1000
  d=divisors(x);
  for i=1:length(d)
    y=d(i);
    if y<x
      if (x-y)*(y^2+1)==2*x*y
        disp([x y])
      end
    end
  end
end

finds

x=10
y=2

x-y=8

harmonic mean:

      2             2*x*y        40
-------------  =   -------   =  ----   =  8
(y/x)+1/(x*y)      y^2 + 1        5


  Posted by Charlie on 2022-09-15 15:06:26
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