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Find From Four 2 (Posted on 2016-06-23) Difficulty: 3 of 5
Each of X and Y is a positive integer such that:

X4 and Y4 share identical last four digits in the same order, and

X-Y = 2016

(A) Find the smallest solution satisfying the given conditions.

(B) Derive the general form of X and Y satisfying the given conditions.

No Solution Yet Submitted by K Sengupta    
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Solution computer solution | Comment 2 of 4 |
  x   y           x^4             y^4           delta y
2258 242      25995354862096  3429742096      
2552 536      42415313391616  82538991616         294
2589 573      44929149932241  107799932241         37
2883 867      69084174032721  565036352721        294
3177 1161     101875290302241 1816891022241       294
3214 1198     106704685401616 2059810521616        37
3508 1492     151439211172096 4955360932096       294
3802 1786     208952922681616 10174798521616      294
3839 1823     217206315402241 11044515642241       37
4133 2117     291784099092721 20085536292721      294
4427 2411     384094499592241 33790050552241      294
4464 2448     397097125871616 35912501231616       37
4758 2742     512504579982096 56528804622096      294
5052 3036     651408419471616 84958545551616      294
5089 3073     670702312122241 89176462602241       37
5383 3367     839648505402721 128520517482721     294

Hypothesis:

Since 294 + 37 + 294 = 625,

y mod 625 = 242, 536 or 573

and of course x = y + 2016


DefDbl A-Z
Dim crlf$


Private Sub Form_Load()
 Form1.Visible = True
 
 
 Text1.Text = ""
 crlf = Chr$(13) + Chr$(10)
 
 For y = 6 To 3600
   DoEvents
   x = y + 2016
   x4$ = Str(x * x * x * x)
   y4$ = Str(y * y * y * y)
   If Right(x4, 4) = Right(y4, 4) Then
      Text1.Text = Text1.Text & x & Str(y) & "    " & x4 & y4 & "       " & x - pr & crlf
      pr = x
   End If
   
 Next
 
 Text1.Text = Text1.Text & " done"
  
End Sub

Edited on June 23, 2016, 7:24 pm
  Posted by Charlie on 2016-06-23 17:02:39

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