Michael's number

Number Theory Level 4

For positive integers \(b>1 \) and \(n\ge 1,\) let \(f_n(b)\) be the largest number (in decimal notation) that has \(n\) digits when expressed in base \(b\). Find the sum of all possible \(n\) such that there exists a value of \(b\) that satisfies \(f_n(b) = 4095.\)

This problem is posed by Michael T.

Details and assumptions

You may choose to read Number Base Representation.


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