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3 coprime unknowns (Posted on 2019-02-04) Difficulty: 3 of 5
Find 3 distinct coprime numbers, all below 50, such that
the square of the first is an average of the cubes of the others.

No Solution Yet Submitted by Ady TZIDON    
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Solution computer solution Comment 2 of 2 |
The first is 42 and the other two are 11 and 13.

The program showed the "first" last:

11 13 42

from

 For a = 1 To 48
 For b = a + 1 To 49
   If gcd(a, b) = 1 Then
 For c = b + 1 To 50
   If gcd(a, c) = 1 And gcd(b, c) = 1 Then
     If c * c = (a * a * a + b * b * b) / 2 Then Text1.Text = Text1.Text & a & Str(b) & Str(c) & crlf
   End If
   DoEvents
 Next
   End If
 Next
 Next
 
with

Function gcd(a, b)
  x = a: y = b
  Do
   q = Int(x / y)
   z = x - q * y
   x = y: y = z
  Loop Until z = 0
  gcd = x
End Function

 



  Posted by Charlie on 2019-02-04 11:55:20
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