Diophantine equations with power sums and Universal Hilbert Sets

Diophantine Properties of Linear Recursive Sequences I

“…(See [NP2,P4].) The situation changed with the papers [CZ1] and [CZ2]. In that papers Corvaja and Zannier proved similar results under quite general conditions.…”

“…Much more interesting are the results of Corvaja and Zannier [CZ1] and [CZ2]. They considered in [CZ1] LRS with integer characteristic roots and proved: Let G n = g 1 a n 1 + · · · + g k a n k , where k ≥ 2, g 1 , .…”

“…They considered in [CZ1] LRS with integer characteristic roots and proved: Let G n = g 1 a n 1 + · · · + g k a n k , where k ≥ 2, g 1 , . .…”

On Diophantine quadruples of Fibonacci numbers

“…Thus, we arrived at the scenario where F b F c + 1 = x 2 has infinitely many integer solutions (b, c, x) with b < c ≤ 4b + 14. Now the Corvaja-Zannier method based on the Subspace Theorem (see [2]) leads to the conclusion that there exists a line parametrized as b = r 1 n + s 1 , c = r 2 n + s 2 for positive integers r 1 , r 2 and integers s 1 , s 2 , such that for infinitely many positive integers n, there exists an integer v n such that…”

“…We take K = Q( √ 5). This is a real quadratic fields with two 1), (1, 2), (1, 3), (1, 4), (2, 0), (2, 1), (2, 2), (2, 3), (3,0), (3,1), (3,2), (4, 0), (4, 1), (5, 0).…”