On polynomials that are sums of two cubes.

Christopher Hooley

Displaying similar documents to “On polynomials that are sums of two cubes.”

Decomposition of an integer as a sum of two cubes to a fixed modulus

David Tsirekidze, Ala Avoyan (2013)

Matematički Vesnik

Similarity:

Almost powers in the Lucas sequence

Yann Bugeaud, Florian Luca, Maurice Mignotte, Samir Siksek (2008)

Journal de Théorie des Nombres de Bordeaux

Similarity:

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 []. 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 [] is not sufficient due to the sizes...

A class of algebraic-exponential congruences modulo $p$ .

Cobeli, C., Vâjâitu, M., Zaharescu, A. (2002)

Acta Mathematica Universitatis Comenianae. New Series

Similarity:

A note on primes p with $σ (p^{m}) = z^{n}$

Maohua Le (1991)

Colloquium Mathematicae

Similarity:

Pretentiousness in analytic number theory

Andrew Granville (2009)

Journal de Théorie des Nombres de Bordeaux

Similarity:

In this report, prepared specially for the program of the , we describe how, in joint work with K. Soundararajan and Antal Balog, we have developed the notion of “pretentiousness” to help us better understand several key questions in analytic number theory.

On the parity of generalized partition functions, III

Fethi Ben Saïd, Jean-Louis Nicolas, Ahlem Zekraoui (2010)

Journal de Théorie des Nombres de Bordeaux

Similarity:

Improving on some results of J.-L. Nicolas [], the elements of the set $𝒜 = 𝒜 (1 + z + z^{3} + z^{4} + z^{5})$ , for which the partition function $p (𝒜, n)$ (i.e. the number of partitions of $n$ with parts in $𝒜$ ) is even for all $n \geq 6$ are determined. An asymptotic estimate to the counting function of this set is also given.

On integers not of the form n - φ (n)

J. Browkin, A. Schinzel (1995)

Colloquium Mathematicae

Similarity:

W. Sierpiński asked in 1959 (see [4], pp. 200-201, cf. [2]) whether there exist infinitely many positive integers not of the form n - φ(n), where φ is the Euler function. We answer this question in the affirmative by proving Theorem. None of the numbers $2^{k} \cdot 509203$ (k = 1, 2,...) is of the form n - φ(n).

The diophantine equation x² + 19 = yⁿ

J. H. E. Cohn (1992)

Acta Arithmetica

Similarity: