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Positive integer solutions of some Diophantine equations in terms of integer sequences
(2019)
In this paper, we define some new number sequences, which we represent as (B n ) , (b n ) , (y n ) and present relations of these new sequences with each other. Then, we give all positive integer solutions of some Diophantine ...
Positive integer solutions of the diophantine equation: X2 -lnxy +(-1)ny2 = ±5r
(2014)
In this paper, we consider the equation X2 -lnxy +(-1)ny2 = ±5r and determine the values of n for which the equation has positive integer solutionsx and y. Moreover, we give all positive integer solutions of the equation ...
Some new identities concerning the Horadam sequence and its companion sequence
(2019)
Let a,b,P, and Q be real numbers with PQ 6≠ 0 and (a,b) 6≠ (0,0). The Horadam sequence (W n ) is defined by W 0 = a, W 1 = b and Wn = PW n-1 + QW n-2 for n ≥ 2. Let the sequence (X n ) be defined by Xn = W n+1 + QW n-1 . ...