All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math
Quadratic and Quartic Query (Posted on 2015-09-06) Difficulty: 3 of 5
Each of A, B, C and D is a nonzero integer such that:

A2 + B2 + C2 = D4, and:
A + B + C = D2

Find the four smallest values of abs(A) + abs(B) + abs(C)

Note: abs(x) is the Absolute Value Function

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.)
Solution computer solution -- the 33 lowest. | Comment 2 of 3 |
The lowest four found were 15, 60, 77 and 79:

   a     b     c     d       sum of abs values
  -3     6     6     3            15
 -12    24    24     6            60
 -14    21    42     7            77
 -15    24    40     7            79
 -27    54    54     9           135
 -48    96    96    12           240
 -39    52   156    13           247
 -56   105   120    13           281
 -56    84   168    14           308
 -60    96   160    14           316
 -75   150   150    15           375
 -80   105   336    19           521
-108   216   216    18           540
 -66    78   429    21           573
-114   190   285    19           589
 -84   105   420    21           609
-126   189   378    21           693
-135   216   360    21           711
-147   294   294    21           735
-192   384   384    24           960
-156   208   624    26           988
-224   420   480    26          1124
-243   486   486    27          1215
-224   336   672    28          1232
-240   384   640    28          1264
-155   186   930    31          1271
-264   385   840    31          1489
-300   600   600    30          1500
 -66    69  1518    39          1653
-363   726   726    33          1815
-231   280  1320    37          1831
-350   525  1050    35          1925
-375   600  1000    35          1975


DefDbl A-Z
Dim crlf$

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

 For tot = 3 To 2000
  For a0 = 1 To tot / 3
   a2 = a0 * a0
   For a = -a0 To a0 Step 2 * a0
  For b0 = a0 To (tot - a0) / 2
   b2 = b0 * b0
   For b = -b0 To b0 Step 2 * b0
   
   c0 = tot - a0 - b0
   c2 = c0 * c0
   For c = -c0 To c0 Step 2 * c0
    
     d4 = a2 + b2 + c2
     d2 = Sqr(d4)
     rt4 = Int(Sqr(d2) + 0.5)
     If rt4 * rt4 * rt4 * rt4 = d4 Then
       d2 = Int(d2 + 0.5)
       If a + b + c = d2 Then
         Text1.Text = Text1.Text & mform(a, "###0") & "  "
         Text1.Text = Text1.Text & mform(b, "###0") & "  "
         Text1.Text = Text1.Text & mform(c, "###0") & "  "
         Text1.Text = Text1.Text & mform(Sqr(d2), "###0") & "  "
         Text1.Text = Text1.Text & "        " & mform(a0 + b0 + c0, "###0") & crlf
         DoEvents
       End If
     End If
   Next
   
   
   Next
  Next
   Next
  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 2015-09-06 14:13:34
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information