Another related paper: "A Golden Pair of Identities in the Theory of Numbers": https://www.ms.uky.edu/~mathclub/Posters/AY_11_12/Schneider.pdf https://www.ms.

Another related paper: "A Golden Pair of Identities in the Theory of Numbers": https://www.ms.uky.edu/~mathclub/Posters/AY_11_12/Schneider.pdf https://www.ms.uky.edu/~mathclub/Posters/AY_11_12/Schneider....