Fibonacci and Lucas numbers with only one distinct digit.
Fibonacci numbers and Diophantine quadruples: generalizations of results of Morgado and Horadam
Fibonacci numbers and Fermat's last theorem
Let Fₙ be the Fibonacci sequence defined by F₀=0, F₁=1, . It is well known that for any odd prime p, where (-) denotes the Legendre symbol. In 1960 D. D. Wall [13] asked whether is always impossible; up to now this is still open. In this paper the sum is expressed in terms of Fibonacci numbers. As applications we obtain a new formula for the Fibonacci quotient and a criterion for the relation (if p ≡ 1 (mod 4), where p ≠ 5 is an odd prime. We also prove that the affirmative answer to...
Fibonacci Numbers in Permutations
Fibonacci Numbers with the Lehmer Property
We show that if m > 1 is a Fibonacci number such that ϕ(m) | m-1, where ϕ is the Euler function, then m is prime
Fibonacci polynomials of order k, multinomial expansions and probability.
Fibrations of low genus, I
Fibrés algébriques sur une surface réelle.
Fibrés quadratiques et composantes connexes réelles.
Field of moduli versus field of definition for cyclic covers of the projective line
We give a criterion, based on the automorphism group, for certain cyclic covers of the projective line to be defined over their field of moduli. An example of a cyclic cover of the complex projective line with field of moduli that can not be defined over is also given.
Fields containing values of algebraic functions
Fields containing values of algebraic functions II (On a conjecture of Schinzel)
Fields generated by linear combinations of roots of unity, II.
Fields of characteristic 2 with prescribed u-invariants.
Fields of Cohomological 2-Dimension Three.
Fields of definition of building blocks with quaternionic multiplication
Fields of definition of -curves
Let be a -curve with no complex multiplication. In this note we characterize the number fields such that there is a curve isogenous to having all the isogenies between its Galois conjugates defined over , and also the curves isogenous to defined over a number field such that the abelian variety Res obtained by restriction of scalars is a product of abelian varieties of GL-type.
Fields of Large Transcendence Degree Generated by Values of Elliptic Functions.
Fields of moduli of three-point -covers with cyclic -Sylow, II
We continue the examination of the stable reduction and fields of moduli of -Galois covers of the projective line over a complete discrete valuation field of mixed characteristic , where has a cyclic-Sylow subgroup of order . Suppose further that the normalizer of acts on via an involution. Under mild assumptions, if is a three-point -Galois cover defined over , then the th higher ramification groups above for the upper numbering of the (Galois closure of the) extension vanish,...
Fields with non-trivial Kaplansky's radical and finite square class number