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Number Theory Level pending

\[ \large 1070_p + 370_p + 721_p + 61_p + 50_p = 603_p + 416_p + 405_p + 503_p + 9_p \]

If \(p \) is an integer such that the numbers in the equation above are written in base \(p\), find the total number of solutions of \(p\).

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