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The famous problem of determining all perfect powers in the Fibonacci sequence ${(F_{n})}_{n \geq 0}$ and in the Lucas sequence ${(L_{n})}_{n \geq 0}$ has recently been resolved [10]. The proofs of those results combine modular techniques from Wiles’ proof of Fermat’s Last Theorem with classical techniques from Baker’s theory and Diophantine approximation. In this paper, we solve the Diophantine equations $L_{n} = q^{a} y^{p}$ , with $a > 0$ and $p \geq 2$ , for all primes $q < 1087$ and indeed for all but $13$ primes $q < 10^{6}$ . Here the strategy of [10] is not sufficient due to the sizes of...

Almost product evaluation of Hankel determinants.

Eğecioğlu, Ömer, Redmond, Timothy, Ryavec, Charles (2008)

The Electronic Journal of Combinatorics [electronic only]

An Addition Theorem for the Elementary Abelian Group of Type (p, p).

Henry B. Mann, Ying Fou Wou (1986)

Monatshefte für Mathematik

An Addition Theorem in a Finite Abelian Group.

Jorgen Cherly (1994)

Mathematica Scandinavica

An addition theorem on the cyclic group $ℤ_{p^{α} q^{β}}$ .

Cao, Huiqin (2006)

The Electronic Journal of Combinatorics [electronic only]

An algorithmic proof theory for hypergeometric (ordinary and "q") multisum/integral indentities.

Herbert S. Wilf, Doron Zeilberger (1992)

Inventiones mathematicae

An Alternative Form of the Functional Equation for Riemann’s Zeta Function, II

Andrea Ossicini (2014)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

This paper treats about one of the most remarkable achievements by Riemann, that is the symmetric form of the functional equation for $ζ (s)$ . We present here, after showing the first proof of Riemann, a new, simple and direct proof of the symmetric form of the functional equation for both the Eulerian Zeta function and the alternating Zeta function, connected with odd numbers. A proof that Euler himself could have arranged with a little step at the end of his paper “Remarques sur un beau rapport entre...

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Affinely self-generating sets and morphisms.

Algebraic independence of real numbers with low density of nonzero digits

Algebraic independence of the values of power series generated by linear recurrences

Algorithme isobarique

Algorithmes pour vérifier la conjecture de Syracuse

Algorithms for Bernoulli and related polynomials.

Algorithms for Bernoulli numbers and Euler numbers.

Algorithmus für Bell'sche Polynome

All Congruent Numbers Less than 2000.

Almost powers in the Lucas sequence

Almost product evaluation of Hankel determinants.

An Addition Theorem for the Elementary Abelian Group of Type (p, p).

An Addition Theorem in a Finite Abelian Group.

An addition theorem on the cyclic group $ℤ_{p^{α} q^{β}}$ .

An algorithmic proof theory for hypergeometric (ordinary and "q") multisum/integral indentities.

An Alternative Form of the Functional Equation for Riemann’s Zeta Function, II

An analogue of the Erdős-Ginzburg-Ziv theorem for quadratic symmetric polynomials.

An analogue of the Thue-Morse sequence.

An application of Catalan numbers on Cayley tree of order 2: Single polygon counting.

An application of Tao's analytic method to restricted sumsets

Currently displaying 241 – 260 of 2472