Decomposition of an integer as a sum of two cubes to a fixed modulus
David Tsirekidze, Ala Avoyan (2013)
Matematički Vesnik
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David Tsirekidze, Ala Avoyan (2013)
Matematički Vesnik
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Yann Bugeaud, Florian Luca, Maurice Mignotte, Samir Siksek (2008)
Journal de Théorie des Nombres de Bordeaux
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The famous problem of determining all perfect powers in the Fibonacci sequence and in the Lucas sequence 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 , with and , for all primes and indeed for all but primes . Here the strategy of [] is not sufficient due to the sizes...
Cobeli, C., Vâjâitu, M., Zaharescu, A. (2002)
Acta Mathematica Universitatis Comenianae. New Series
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Maohua Le (1991)
Colloquium Mathematicae
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Andrew Granville (2009)
Journal de Théorie des Nombres de Bordeaux
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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.
Fethi Ben Saïd, Jean-Louis Nicolas, Ahlem Zekraoui (2010)
Journal de Théorie des Nombres de Bordeaux
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Improving on some results of J.-L. Nicolas [], the elements of the set , for which the partition function (i.e. the number of partitions of with parts in ) is even for all are determined. An asymptotic estimate to the counting function of this set is also given.
J. Browkin, A. Schinzel (1995)
Colloquium Mathematicae
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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 (k = 1, 2,...) is of the form n - φ(n).
J. H. E. Cohn (1992)
Acta Arithmetica
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