Zeckendorf Representation of Integer shifted Left/Historical Note

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Historical Note on Zeckendorf Representation of Integer shifted Left

According to Donald E. Knuth in his The Art of Computer Programming: Volume 1: Fundamental Algorithms, 3rd ed. of $1997$, this result was demonstrated by Yuri Vladimirovich Matiyasevich in $1990$, but no further details are given.