# Perfect Squares' Squares' Properties

**Number Theory**Level 3

\(n\) is *any* integer. Denote the sum of all the possible unit digits of \(n^4\) as \(S\). Find \(504\cdot S^{-1}\).

**Details & Assumptions**:

- \(S^{-1}\) denotes the multiplicative inverse.

\(n\) is *any* integer. Denote the sum of all the possible unit digits of \(n^4\) as \(S\). Find \(504\cdot S^{-1}\).

**Details & Assumptions**:

- \(S^{-1}\) denotes the multiplicative inverse.

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