The sets that meet the criterion that all of a, b and c be different are marked with an * below.  The other sets satisfy the equation but contain at least one equality between number pairs.

2 2 2

9 18 9

32 32 16

28 84 28

70 105 35 *

162 162 54

65 260 65

144 288 72 *

273 364 91 *

126 630 126

266 665 133 *

512 512 128

469 603 134 *

456 760 152 *

455 1001 182 *

217 1302 217

793 854 183 *

756 945 189 *

448 1344 224 *

737 1072 201 *

730 1241 219 *

729 1458 243 *

417 1807 278 *

728 1729 273 *

1250 1250 250

344 2408 344

721 2060 309 *

1120 1680 280 *

702 2457 351 *

211 3165 422 *

665 2926 399 *

1110 2590 370 *

1705 2046 341 *

604 3473 453 *

1628 2849 407 *

513 4104 513

1136 3905 497 *

2592 2592 432

1040 4160 520 *

386 4825 579 *

2340 3276 468 *

217 5642 651 *

1617 4312 539 *

2304 4608 576 *

3354 3913 559 *

730 6570 730

1474 6633 737 *

3185 5096 637 *

3666 5170 658 *

2268 6804 756 *

4802 4802 686

4368 5824 728 *

3172 7137 793 *

1001 10010 1001

4270 7686 854 *

2016 10080 1008 *

5985 6840 855 *

3081 10270 1027 *

5670 8505 945 *

4256 10640 1064 *

1332 14652 1332

8192 8192 1024

7770 8806 1036 *

5625 11250 1125 *

7504 9648 1072 *

2678 14729 1339 *

7358 10754 1132 *

4074 14938 1358 *

7296 12160 1216 *

...

manually terminated

DefDbl A-Z

Dim crlf$

Private Sub Form_Load()

 Form1.Visible = True

 

 

 Text1.Text = ""

 crlf = Chr$(13) + Chr$(10)

 

 For tot = 3 To 9999999

    For a = 1 To tot / 2

      a3 = a * a * a

      b = tot - a

      b3 = b * b * b

      c4 = a3 + b3

      c = Int(Sqr(Sqr(c4)))

      If c * c * c * c = c4 Then

        Text1.Text = Text1.Text & a & Str(b) & Str(c)

        If b > a And c <> b And c <> a Then Text1.Text = Text1.Text & " *"

        Text1.Text = Text1.Text & crlf

      End If

      DoEvents

    Next

 Next tot

 

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

  

End Sub