EuDML | Browse

We give the answer to the question in the title by proving that $L_{18} = 5778 = 5555 + 222 + 1$ is the largest Lucas number expressible as a sum of exactly three repdigits. Therefore, there are many Lucas numbers which are sums of three repdigits.

Catalan’s conjecture

Yuri F. Bilu (2002/2003)

Séminaire Bourbaki

The subject of the talk is the recent work of Mihăilescu, who proved that the equation $x^{p} - y^{q} = 1$ has no solutions in non-zero integers $x, y$ and odd primes $p, q$ . Together with the results of Lebesgue (1850) and Ko Chao (1865) this implies the celebratedconjecture of Catalan (1843): the only solution to $x^{u} - y^{v} = 1$ in integers $x, y > 0$ and $u, v > 1$ is $3^{2} - 2^{3} = 1$ . Before the work of Mihăilescu the most definitive result on Catalan’s problem was due to Tijdeman (1976), who proved that the solutions of Catalan’s equation are bounded by an absolute...

Character coordinates and annihilators of cyclotomic numbers.

Kurt Girstmair (1987)

Manuscripta mathematica

Characteristic approximation properties of quadratic irrationals.

Jurkat, W.B., Peyerimhoff, A. (1978)

International Journal of Mathematics and Mathematical Sciences

Characterizations of groups generated by Kronecker sets

András Biró (2007)

Journal de Théorie des Nombres de Bordeaux

In recent years, starting with the paper [B-D-S], we have investigated the possibility of characterizing countable subgroups of the torus $T = R / Z$ by subsets of $Z$ . Here we consider new types of subgroups: let $K \subseteq T$ be a Kronecker set (a compact set on which every continuous function $f : K \to T$ can be uniformly approximated by characters of $T$ ), and $G$ the group generated by $K$ . We prove (Theorem 1) that $G$ can be characterized by a subset of $Z^{2}$ (instead of a subset of $Z$ ). If $K$ is finite, Theorem 1 implies our earlier result...

Closed Curves and Geodesics with Two Self-Intersections on the Punctured Torus.

D. Crisp, S. Dziadosz, D.J. Garity (1998)

Monatshefte für Mathematik

Collatz cycles with few descents

T. Brox (2000)

Acta Arithmetica

Comments on some formulae of Ramanujan

Emil Grosswald (1972)

Acta Arithmetica

Comments on the fractional parts of Pisot numbers

Toufik Zaïmi, Mounia Selatnia, Hanifa Zekraoui (2015)

Archivum Mathematicum

Let $L (θ, λ)$ be the set of limit points of the fractional parts ${λ θ^{n}}$ , $n = 0, 1, 2, \dots$ , where $θ$ is a Pisot number and $λ \in ℚ (θ)$ . Using a description of $L (θ, λ)$ , due to Dubickas, we show that there is a sequence ${(λ_{n})}_{n \geq 0}$ of elements of $ℚ (θ)$ such that $Card (L (θ, λ_{n})) < Card (L (θ, λ_{n + 1}))$ , $\forall$ $n \geq 0$ . Also, we prove that the...

Commutative algebraic groups and p-adic linear forms

Clemens Fuchs, Duc Hiep Pham (2015)

Acta Arithmetica

Let G be a commutative algebraic group defined over a number field K that is disjoint over K from $_{a}$ and satisfies the condition of semistability. Consider a linear form l on the Lie algebra of G with algebraic coefficients and an algebraic point u in a p-adic neighbourhood of the origin with the condition that l does not vanish at u. We give a lower bound for the p-adic absolute value of l(u) which depends up to an effectively computable constant only on the height of the linear form, the height...

Currently displaying 261 – 280 of 1536

Previous Page 14 Next

Displaying 261 – 280 of 1536

Brownian motion, approximation of functions, and Fourier analysis

$C$ -uniform distribution of entire functions

Calculation of improper integrals using uniformly distributed sequences

Calculs sur des suites récurrentes linéaires

Can a Lucas number be a sum of three repdigits?

Catalan’s conjecture

Character coordinates and annihilators of cyclotomic numbers.

Characteristic approximation properties of quadratic irrationals.

Characterizations of groups generated by Kronecker sets

Closed Curves and Geodesics with Two Self-Intersections on the Punctured Torus.

Collatz cycles with few descents

Comments on some formulae of Ramanujan

Comments on the fractional parts of Pisot numbers

Commutative algebraic groups and p-adic linear forms

Complément à : «Sur l’approximation de $π$ par des nombres algébriques particuliers»

Complete systems of addition laws on Abelian varieties.

Complex dimensions of self-similar fractal strings and Diophantine approximation.

Computing all elements of given index in sextic fields with a cubic subfield

Computing integral points on elliptic curves

Computing the lower bound for linear forms in logarithms

Currently displaying 261 – 280 of 1536