This is the first in a series of papers whereby we combine the classical approach to
exponential Diophantine equations (linear forms in logarithms, Thue equations, etc.) with a …

We show how the Gelfond-Baker theory and diophantine approximation techniques can be
applied to solve explicitly the diophantine equation ${G_n}= wp_1^{{m_1}}\cdots p_t^{{m_t}} …

Fibonacci numbers at most one away from a perfect power Page 1 Elem. Math. 63 (2008) 65 –
75 0013-6018/08/020065-11 c Swiss Mathematical Society, 2008 Elemente der Mathematik …

Rn= xq(2) in integers n, x, q subject to| x|> 1, q≥ 2. Shorey and Stewart [8] and
independently Pethö [4] proved that (2) has only finitely many effectively computable …

In this paper we develop a method for computing all small solutions (ie with coordinates of
absolute value< 10 7) of index form equations in totally real biquadratic number fields. If the …

Let (F m) m≥ 0 be the Fibonacci sequence given by F 0= 0, F 1= 1 and F m+ 2= F m+ 1+ F
m, for all m≥ 0. In Castillo (2015), it is conjectured that 2, 5 and 34 are the only Fibonacci …

In this paper, we consider the sequence of balancing and Lucas balancing numbers. The
balancing numbers B_n B n are given by the recurrence B_n= 6 B_ n-1-B_ n-2 B n= 6 B n-1 …

Suppose that is a Lucas sequence, and suppose that l 1,…, lt are primes. We show that the
equation has only finitely many solutions. Moreover, we explain a practical method of …

Polynomial Values in Linear Recurrences, II* Page 1 JOURNAL OF NUMBER THEORY 24, 47-53
(1986) Polynomial Values in Linear Recurrences, II* ISTVAN NEMES AND ATTILA PETH …

There is indeed not much relation between the Fibonacci numbers and the Arctic Ocean, but
I thought that this title would excite your curiosity for my lecture. You will be disappointed if …