Decomposition of an integer as a sum of two cubes to a fixed modulus
David Tsirekidze, Ala Avoyan (2013)
Matematički Vesnik
Similarity:
David Tsirekidze, Ala Avoyan (2013)
Matematički Vesnik
Similarity:
Moujie Deng, G. Cohen (2000)
Colloquium Mathematicae
Similarity:
Let a, b, c be relatively prime positive integers such that . Jeśmanowicz conjectured in 1956 that for any given positive integer n the only solution of in positive integers is x=y=z=2. If n=1, then, equivalently, the equation , for integers u>v>0, has only the solution x=y=z=2. We prove that this is the case when one of u, v has no prime factor of the form 4l+1 and certain congruence and inequality conditions on u, v are satisfied.
J. H. E. Cohn (1992)
Acta Arithmetica
Similarity:
Wayne McDaniel (1993)
Colloquium Mathematicae
Similarity:
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 (k = 1, 2,...) is of the form n - φ(n).
Lewittes, Joseph, Kolyvagin, Victor (2010)
The New York Journal of Mathematics [electronic only]
Similarity:
Antone Costa (1992)
Acta Arithmetica
Similarity:
Yasushige Watase (2014)
Formalized Mathematics
Similarity:
This article provides a formalized proof of the so-called “the four-square theorem”, namely any natural number can be expressed by a sum of four squares, which was proved by Lagrange in 1770. An informal proof of the theorem can be found in the number theory literature, e.g. in [14], [1] or [23]. This theorem is item #19 from the “Formalizing 100 Theorems” list maintained by Freek Wiedijk at http://www.cs.ru.nl/F.Wiedijk/100/.
Timoshenko, E.A. (2004)
Sibirskij Matematicheskij Zhurnal
Similarity: