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 Cube root sum equality puzzle (Posted on 2015-06-09)
Find all pairs (a,b) of positive integers that satisfy this equation:

(∛A + ∛B -1)2 = 49 + 20*∛6

 No Solution Yet Submitted by K Sengupta No Rating

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 computer solution | Comment 1 of 2
DefDbl A-Z
Dim crlf\$

Form1.Visible = True

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

rhs = 49 + 20 * 6 ^ (1 / 3)
sr = Sqr(rhs)

For a = 1 To 1100
b = Int((sr + 1 - a ^ (1 / 3)) ^ 3 + 0.5)
If b > 0 Then
lhs = (a ^ (1 / 3) + b ^ (1 / 3) - 1) ^ 2
diff = Abs(rhs - lhs)
If diff / rhs < 0.000001 Then
Text1.Text = Text1.Text & a & Str(b) & "    "
Text1.Text = Text1.Text & lhs & Str(rhs) & crlf
DoEvents
End If
End If
Next

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

End Sub

finds

`A   B            LHS            RHS  48 288    85.3424118566428 85.3424118566428288 48    85.3424118566428 85.3424118566428`

(48,288) and its reverse, (288,48).

 Posted by Charlie on 2015-06-09 15:54:15

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