Diophantine triples with values in binary recurrences
نویسندگان
چکیده
منابع مشابه
Diophantine Equations Related with Linear Binary Recurrences
In this paper we find all solutions of four kinds of the Diophantine equations begin{equation*} ~x^{2}pm V_{t}xy-y^{2}pm x=0text{ and}~x^{2}pm V_{t}xy-y^{2}pm y=0, end{equation*}% for an odd number $t$, and, begin{equation*} ~x^{2}pm V_{t}xy+y^{2}-x=0text{ and}text{ }x^{2}pm V_{t}xy+y^{2}-y=0, end{equation*}% for an even number $t$, where $V_{n}$ is a generalized Lucas number. This pape...
متن کاملStrong Diophantine Triples
We prove that there exist infinitely many triples a, b, c of non-zero rationals with the property that a + 1, b + 1, c + 1, ab + 1, ac + 1 and bc + 1 are perfect squares.
متن کاملBalancing diophantine triples
In this paper, we show that there are no three distinct positive integers a, b and c such that ab + 1, ac + 1, bc + 1 all are balancing numbers.
متن کاملDiophantine Triples with Values in the Sequences of Fibonacci and Lucas Numbers
Let FL = {1, 2, 3, 4, 5, 7, 8, 11, 13, 18, 21, . . .} be the set consisting of all Fibonacci and Lucas numbers with positive subscripts. We find all triples (a, b, c) of positive integers a < b < c such that ab + 1, ac+ 1, bc+ 1 are all members of FL.
متن کاملBalancing Diophantine triples with distance 1
For a positive real number w let the Balancing distance ‖w‖B be the distance from w to the closest Balancing number. The Balancing sequence is defined by the initial values B0 = 0, B1 = 1 and by the binary recurrence relation Bn+2 = 6Bn+1 − Bn , n ≥ 0. In this paper, we show that there exist only one positive integer triple (a, b, c) such that the Balancing distances ‖ab‖B , ‖ac‖B and ‖bc‖B all...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE
سال: 2009
ISSN: 2036-2145,0391-173X
DOI: 10.2422/2036-2145.2008.4.01