In this paper, we look at a diophantine equation of the form un = x y , where (un)n≥0 is a binary recurrent sequence of integers. We show that if the pair of integers (x, y) belongs to a fixed line of the Pascal triangle, then the above equation has only finitely many positive integer solutions (n, x, y).
Luca, F., Pappalardi, F. (2005). Members of binary recurrences on lines of the Pascal triangle. PUBLICATIONES MATHEMATICAE, 67, 103-113.
Members of binary recurrences on lines of the Pascal triangle
PAPPALARDI, FRANCESCO
2005-01-01
Abstract
In this paper, we look at a diophantine equation of the form un = x y , where (un)n≥0 is a binary recurrent sequence of integers. We show that if the pair of integers (x, y) belongs to a fixed line of the Pascal triangle, then the above equation has only finitely many positive integer solutions (n, x, y).File in questo prodotto:
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