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Results of this paper concern $n$-determinants which we defined in the paper\cite{jan}. In the paper \cite{jabo}, $2$-determinants are considered. In thispaper, we extend results from \cite{jabo} on $n$-determinants by proving thatCassini, d'Ocagne, Catalan and Vajda identities may be extended to hold for$n$-step Fibonacci numbers.

Cassini, d'Ocagne, and Vajda identities for n-step Fibonacci numbers