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Square Sum and Square Multiple (Posted on 2015-09-13) Difficulty: 3 of 5
Find the four smallest positive integer solutions to this equation:

X2 + Y2 = 2017*Z2

Note: “Four smallest solutions” mean the solutions with the four smallest values of X+Y.

No Solution Yet Submitted by K Sengupta    
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Solution An extended list -- Using Visual Basic Comment 2 of 2 |
    x    y  z
    9   44  1
   18   88  2
   27  132  3
   36  176  4
   45  220  5
   96  203  5
  149  168  5
   54  264  6
   63  308  7
   72  352  8
   81  396  9
   90  440 10
   99  484 11
  192  406 10
  298  336 10
  108  528 12
  112  573 13
  117  572 13
  126  616 14
  135  660 15
  328  483 13
  144  704 16
  288  609 15
  153  748 17
  217  732 17
  447  504 15
  162  792 18
  171  836 19
  180  880 20
  487  588 17
  189  924 21
  198  968 22
  384  812 20
   92 1119 25
  207 1012 23
  596  672 20
  216 1056 24
  225 1100 25
  224 1146 26
  234 1144 26
  243 1188 27
  252 1232 28
  480 1015 25
  524  993 25
  261 1276 29
  745  840 25
  270 1320 30
  656  966 26
  279 1364 31
  288 1408 32
  297 1452 33
  576 1218 30
  691 1104 29
  306 1496 34
  744 1069 29
  315 1540 35
  213 1648 37
   36 1841 41
  434 1464 34
  894 1008 30
  324 1584 36
  333 1628 37
  342 1672 38
  336 1719 39
  351 1716 39
  672 1421 35
  360 1760 40
  974 1176 34
  369 1804 41
 1043 1176 35
  378 1848 42
  843 1432 37
  387 1892 43
  396 1936 44
  405 1980 45
  768 1624 40
  184 2238 50
  984 1449 39
  756 1679 41
  414 2024 46
  423 2068 47
 1192 1344 40
  432 2112 48
  441 2156 49
  450 2200 50
  864 1827 45
  459 2244 51
  448 2292 52
  468 2288 52
   56 2739 61
  477 2332 53
  651 2196 51
 1341 1512 45
  486 2376 54
  495 2420 55
  504 2464 56
  960 2030 50
  513 2508 57
 1048 1986 50
  137 2916 65

As per Steve Herman's comment, each X and Y can be interchanged.  
  
  
  
DefDbl A-Z
Dim crlf$


Private Sub Form_Load()
 Form1.Visible = True
 
 Text1.Text = ""
 crlf = Chr$(13) + Chr$(10)

 For tot = 2 To 10000
   For x = 1 To tot / 2
     y = tot - x
     z2 = (x * x + y * y) / 2017
     If z2 = Int(z2) Then
       z = Int(Sqr(z2) + 0.5)
       If z * z = z2 Then
         Text1.Text = Text1.Text & mform(x, "####0") & mform(y, "####0") & mform(z, "##0") & crlf
         DoEvents
         ct = ct + 1
         If ct > 99 Then Exit Sub
       End If
     End If
   Next
 Next


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

Function mform$(x, t$)
  a$ = Format$(x, t$)
  If Len(a$) < Len(t$) Then a$ = Space$(Len(t$) - Len(a$)) & a$
  mform$ = a$
End Function
  


  Posted by Charlie on 2015-09-13 14:54:43
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