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 Find From Four 2 (Posted on 2016-06-23)
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 No Rating

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 computer solution | Comment 2 of 4 |
`  x   y           x^4             y^4           delta y2258 242      25995354862096  3429742096      2552 536      42415313391616  82538991616         2942589 573      44929149932241  107799932241         372883 867      69084174032721  565036352721        2943177 1161     101875290302241 1816891022241       2943214 1198     106704685401616 2059810521616        373508 1492     151439211172096 4955360932096       2943802 1786     208952922681616 10174798521616      2943839 1823     217206315402241 11044515642241       374133 2117     291784099092721 20085536292721      2944427 2411     384094499592241 33790050552241      2944464 2448     397097125871616 35912501231616       374758 2742     512504579982096 56528804622096      2945052 3036     651408419471616 84958545551616      2945089 3073     670702312122241 89176462602241       375383 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\$

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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