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Just count them ! (Posted on 2019-04-09) Difficulty: 2 of 5
How many integer solutions has the following equation:
sqrt(x)+sqrt(y)=sqrt(3888)?

Assume x>y.

See The Solution Submitted by Ady TZIDON    
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Solution computer solution | Comment 1 of 2
DefDbl A-Z
Dim crlf$

Private Sub Form_Load()
 Text1.Text = ""
 crlf$ = Chr(13) + Chr(10)
 Form1.Visible = True
 DoEvents
 
 For x = 0 To 3888
   For y = 0 To x
      summ = Sqr(x) + Sqr(y)
      diff = Abs(Sqr(3888) - summ)
      If diff < 0.0000000001 Then
          Text1.Text = Text1.Text & x & Str(y) & crlf
          ct = ct + 1
      End If
   Next
 Next
 
 Text1.Text = Text1.Text & ct & " done"
End Sub

lists integral solutions to sqrt(x)+sqrt(y)=sqrt(3888):

 972 972
1083 867
1200 768
1323 675
1452 588
1587 507
1728 432
1875 363
2028 300
2187 243
2352 192
2523 147
2700 108
2883 75
3072 48
3267 27
3468 12
3675 3
3888 0


There are 19 solutions, but the first one listed has x=y rather than x>y, so the answer to the puzzle is 18.


  Posted by Charlie on 2019-04-09 10:55:30
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