It could be PLAGIARISM. Let's just say...involuntary.

See Problem 29052, from GMB 2-2025.

A similar problem was also published in a book:
Paul RADOVICI-MARCULESCU : "Probleme de Teoria Elementara a Numerelor"...(see in list)

On page 87, Problem 4.7 appears, which does pretty much the same thing, about a similar sequences.

The solution appears on page 95. But the statement also required a generalization which also appears in this solution.

More I DO NOT COMMENT here, if you want you can visit my blog ogeometrie-cip.