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Cubic Diophantine Conclusion (Posted on 2016-04-22) Difficulty: 3 of 5
Each of A, B and C is a positive integer that satisfies this equation:

A3 + B3 = 31C3

Find the smallest value of A+B+C

No Solution Yet Submitted by K Sengupta    
Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts computer exploration | Comment 1 of 9
DefDbl A-Z
Dim crlf$


Private Sub Form_Load()
 Form1.Visible = True
 
 Text1.Text = ""
 crlf = Chr$(13) + Chr$(10)
 
 For tot = 2 To 99999
   For a = 1 To tot / 2
    DoEvents
     b = tot - a
     lhs = a * a * a + b * b * b
     c = Int((lhs / 31) ^ (1 / 3) + 0.5)
     If c * c * c * 31 = lhs Then
       Text1.Text = Text1.Text & a & Str(b) & Str(c) & "    " & lhs & Str(a + b + c) & crlf
     End If
   Next
 Next

 
 Text1.Text = Text1.Text & crlf & " done"
  
End Sub

finds no solution for a+b under 100,000, even without c.

Edited on April 22, 2016, 11:13 am
  Posted by Charlie on 2016-04-22 11:11:58

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