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 More than linear (Posted on 2015-06-30)
Find all possible positive integer solutions to this equation:

AN - BN = 2015, whenever N ≥ 2

Note: The common exponent must also be an integer.

 No Solution Yet Submitted by K Sengupta No Rating

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 computer solution Comment 1 of 1
`a      b  n48    17 284    71 2204  199 21008 1007 214     9 3`
`from`
```DefDbl A-Z
Dim crlf\$

Form1.Visible = True

Text1.Text = ""
crlf = Chr\$(13) + Chr\$(10)

For n = 2 To 11
tot = 3
Do
'Text1.Text = Text1.Text & tot & crlf
DoEvents
noSoln = 0
soln = 0
For b = Int(tot / 2) To 1 Step -1
a = tot - b
aton = Int(a ^ n + 0.5)
bton = Int(b ^ n + 0.5)
If aton > maxnum Then maxnum = aton
If bton > maxnum Then maxnum = bton
diff = aton - bton
If diff > 2015 And a - b = 1 Then noSoln = 1: Exit For
If diff > 2015 Then Exit For
If diff = 2015 Then
Text1.Text = Text1.Text & a & Str(b) & Str(n) & crlf
Exit For
End If
Next
tot = tot + 1
Loop Until noSoln
Next

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

End Sub

```

 Posted by Charlie on 2015-06-30 16:19:44

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