In this paper, we define a Lucas-Lehmer type sequence denoted by (L-n)(n=0)(infinity), and show that there are no integers 0 < a < b < c such that ab + 1, ac + 1 and bc + 1 all are terms of the sequence
We prove that for $n$ > 30, every $n$-th Lucas and Lehmer number has a primitive divisor. This allow...
We prove that for~${n>30}$, every~$n$-th Lucas and Lehmer number has a primitive divisor. This allow...
We prove that there are only finitely many terms of a non-degenerate linear recurrence sequence whic...
In this paper, we show that if (u<SUB>n</SUB>)<SUB>n≥1</SUB> is a Lucas sequence, then the Diophanti...
AbstractIn this paper, we show that if (un)n⩾1 is a Lucas sequence, then the Diophantine equation un...
In this paper, we consider binomial triple sums families whose coefficients are chosen as the Lucas ...
Let P and Q be nonzero integers. Generalized Fibonacci and Lucas sequences are defined as follows: U...
In this paper, we show that there are no three distinct positive integers a, b, c such that ab+1, ac...
In this paper, we shall study the Diophantine equation un = R(m)P(m)Q(m), where un is a Lucas sequen...
A Lucas sequence is a binary recurrence sequences that includes as special cases, the Pell, the asso...
AbstractLet u=(un)n=0∞ be a Lucas sequence, that is a binary linear recurrence sequence of integers ...
β denote the zeros of x2 −√Rx+Q. In 1930, D. H. Lehmer [4] extended the arithmetic theory of Lucas s...
AbstractWe prove that there are only finitely many terms of a non-degenerate linear recurrence seque...
n=0 is given by the recurrence un = 2un−1 + un−2 with initial condition u0 = 0, u1 = 1 and its assoc...
summary:Let $(L_n)_{n\geq 0}$ be the Lucas sequence. We show that the Diophantine equation $ L_n-L_m...
We prove that for $n$ > 30, every $n$-th Lucas and Lehmer number has a primitive divisor. This allow...
We prove that for~${n>30}$, every~$n$-th Lucas and Lehmer number has a primitive divisor. This allow...
We prove that there are only finitely many terms of a non-degenerate linear recurrence sequence whic...
In this paper, we show that if (u<SUB>n</SUB>)<SUB>n≥1</SUB> is a Lucas sequence, then the Diophanti...
AbstractIn this paper, we show that if (un)n⩾1 is a Lucas sequence, then the Diophantine equation un...
In this paper, we consider binomial triple sums families whose coefficients are chosen as the Lucas ...
Let P and Q be nonzero integers. Generalized Fibonacci and Lucas sequences are defined as follows: U...
In this paper, we show that there are no three distinct positive integers a, b, c such that ab+1, ac...
In this paper, we shall study the Diophantine equation un = R(m)P(m)Q(m), where un is a Lucas sequen...
A Lucas sequence is a binary recurrence sequences that includes as special cases, the Pell, the asso...
AbstractLet u=(un)n=0∞ be a Lucas sequence, that is a binary linear recurrence sequence of integers ...
β denote the zeros of x2 −√Rx+Q. In 1930, D. H. Lehmer [4] extended the arithmetic theory of Lucas s...
AbstractWe prove that there are only finitely many terms of a non-degenerate linear recurrence seque...
n=0 is given by the recurrence un = 2un−1 + un−2 with initial condition u0 = 0, u1 = 1 and its assoc...
summary:Let $(L_n)_{n\geq 0}$ be the Lucas sequence. We show that the Diophantine equation $ L_n-L_m...
We prove that for $n$ > 30, every $n$-th Lucas and Lehmer number has a primitive divisor. This allow...
We prove that for~${n>30}$, every~$n$-th Lucas and Lehmer number has a primitive divisor. This allow...
We prove that there are only finitely many terms of a non-degenerate linear recurrence sequence whic...
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