Combinatorial numbers in binary recurrences
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In this paper, we prove that the generalized Cullen numbers, Cn(s, l) := sn ·2+ l, where l is an integer and s := (sn)n≥0 is a sequence of integers satisfying log |sn| c1 we have log |Q| > |P |2 . Finally, we find all Cullen numbers, i.e., numbers of the form n ·2+1 and all Wooda
In this paper, we look at a diophantine equation of the form un = ( x y ) , where (un)n≥0 is a binary recurrent sequence of integers. We show that if the pair of integers (x, y) belongs to a fixed line of the Pascal triangle, then the above equation has only finitely many positiv
PED partitions are with even parts distinct while odd unrestricted. Similarly, POD have In [16] several recurrence relations for the number of n proved analytically. They similar to relation given by Euler's pentagonal theorem. We provide combinatorial proofs all these theorems a
We provide two combinatorial proofs that linear recurrences with constant coefficients have a closed form based on the roots of its characteristic equation. The proofs employ sign-reversing involutions on weighted tilings.
We use a refined version of Roth’s Lemma, proved with the help of Faltings’ Product Theorem, in order to give an upper bound for the multiplicity of a binary linear recurrence. Résumé Nous utilisons une version du Lemme de Roth, provenant du Théorème du Produit de Faltings, pour
“Combinatorial number theory”, in very loose terms, can be described as an area of mathematics which is a cross between combinatorics and number theory. More precisely, the area concerns structures of integers (or similar sets), with some number theoretic properties, which can be