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4 numbers make 5 squares (Posted on 2016-06-30) Difficulty: 3 of 5
Find four whole numbers such that:

each pairwise sum is a perfect square and
the sum of all four is a perfect square.

No Solution Yet Submitted by Jer    
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re(2): computer solution and discussion | Comment 3 of 10 |
(In reply to re: computer solution and discussion by Jer)

I've expanded the search, and limited to integers to speed things up, but all found where a<>b and c<>d still have b = c.


-968 968 968 2057
-968 968 968 14657
-968 968 968 58568
-943 1568 1568 2032
-904 5000 5000 58504
-882 882 882 2482
-882 882 882 4018
-882 882 882 21618
-882 882 882 194482
-800 800 800 881
-800 800 800 1700
-800 800 800 2564
-800 800 800 6425
-800 800 800 10016
-800 800 800 40004
-800 800 800 160001
-727 1352 1352 2248
-722 722 722 130322
-712 2312 2312 3313
-648 648 648 873
-648 648 648 1377
-648 648 648 2952
-648 648 648 6577
-648 648 648 11673
-648 648 648 26248
-648 648 648 104977
-631 800 800 6256
-604 800 800 1504
-584 9800 9800 51209
-578 578 578 83522
-544 43808 43808 49828
-542 3042 3042 11358
-512 512 512 1088
-512 512 512 4112
-512 512 512 16388
-512 512 512 65537
-479 648 648 6408
-450 450 450 706
-450 450 450 2050
-450 450 450 5634
-450 450 450 50626
-392 392 392 833
-392 392 392 2417
-392 392 392 9608
-392 392 392 38417
-338 338 338 28562
-288 288 288 337
-288 288 288 388
-288 288 288 612
-288 288 288 1312
-288 288 288 2313
-288 288 288 5188
-288 288 288 20737
-263 1352 1352 1784
-254 450 450 1854
-242 242 242 14642
-226 1250 1250 14626
-200 200 200 425
-200 200 200 641
-200 200 200 2504
-200 200 200 10001
-162 162 162 738
-162 162 162 6562
-151 200 200 376
-136 10952 10952 12457
-128 128 128 272
-128 128 128 1028
-128 128 128 4097
-98 98 98 2402
-72 72 72 97
-72 72 72 153
-72 72 72 328
-72 72 72 1297
-72 20808 20808 74056
-50 50 50 626
-32 32 32 68
-32 32 32 257
-18 18 18 82
-18 5202 5202 18514
-8 8 8 17
1 288 288 20448
4 1152 1152 81792
9 2592 2592 184032
257 968 968 13432
322 2178 2178 12222
496 800 800 5129

 Text1.Text = ""
 crlf = Chr$(13) + Chr$(10)
 
 lim = 99999
 lim2 = lim * lim
 
 For a = -1000 To 1000
  If a > 0 Then lval = Int(Sqr(2 * a)) Else lval = 0
  For sr1 = lval To Sqr(a + lim)
     b = sr1 * sr1 - a
     If b > 0 Then
     For sr2 = Int(Sqr(2 * b)) To Sqr(b + lim)
     DoEvents
       c = sr2 * sr2 - b
       If a + c >= 0 Then
       sr = Int(Sqr(a + c) + 0.5)
       If sr * sr = a + c Then
         For sr3 = Int(Sqr(2 * c)) To Sqr(2 * lim)
           d = sr3 * sr3 - c
            If d + a >= 0 Then
              sr = Int(Sqr(a + d) + 0.5)
              If sr * sr = a + d Then
                sr = Int(Sqr(b + d) + 0.5)
                If sr * sr = b + d Then
                  sr = Int(Sqr(a + b + b + d) + 0.5)
                  If sr * sr = a + b + c + d Then
                   If a <> b And c <> d Then
                     Text1.Text = Text1.Text & a & Str(b) & Str(c) & Str(d)
               '      If Abs(a) <> b And c <> d Then Text1.Text = Text1.Text & "        *******"
                     Text1.Text = Text1.Text & crlf
                   End If
                  End If
                End If
              End If
            End If
         Next
       End If
       End If
     Next sr2
     End If
  Next sr1
 Next

  Posted by Charlie on 2016-06-30 22:36:30
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