Mind Blowing!

\[973x-1234y=2015\]

If (\(x\),\(y\)) is the least positive integral solution of the equation above then find the number of digits in \(x^{y}\).

Details and Assumptions:

  • \(\log _{ 10 }{ 3 } =0.4771212547197...\)

  • \(\log _{ 10 }{ 131 } =2.117271295656...\)

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