Results 11 to 20 of about 141 (106)
On a few Diophantine equations, in particular, Fermat's last theorem
International Journal of Mathematics and Mathematical Sciences, 2003 This is a survey on Diophantine equations, with the purpose being to give the flavour of some known results on the subject and to describe a few open problems.
C. Levesque
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Extending the plane trigonometric proof of Fermat's Last Theorem to the case n=3 [PDF]
Notes on Number Theory and Discrete MathematicsWe extend the plane trigonometric approach that we used to prove the case n=4 of Fermat's Last Theorem, to the case n=3. We show that all real positive triplets satisfying a^ϕ+b^ϕ=cϕ for ϕ>1 are triangles. As in the case of n=4, we equate the Pythagorean
Giri Prabhakar
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International Journal of Mathematics and Mathematical Sciences, 1987 In this note we discuss recent progress concerning powerful numbers, raise new questions and show that solutions to existing open questions concerning powerful numbers would yield advancement of solutions to deep, long-standing problems such as Fermat's ...
R. A. Mollin
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SPECIAL COURSE FOR SCHOOLCHILDREN: PROOF OF FERMAT'S GREAT THEOREM BY EXAMPLE x^3+y^3+z^3=0 [PDF]
Vestnik Issyk-Kulʹskogo universitetaIt is difficult to find a person among mathematicians who is not familiar with and does not study the solution of the equation x^2+y^2+z^2=0, or x^3+y^3+z^3=0 in integers.
Srashidinov A.
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MathematicsThe Mathematics Editorial Office retracts the article entitled “On the Nature of Some Euler’s Double Equations Equivalent to Fermat’s Last Theorem [...]
Andrea Ossicini
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Rational points on even‐dimensional Fermat cubics
Transactions of the London Mathematical Society, Volume 13, Issue 1, December 2026.Abstract We show that even‐dimensional Fermat cubic hypersurfaces are rational over any field of characteristic not equal to three, by constructing explicit rational parameterizations with polynomials of low degree. As a byproduct of our rationality constructions, we obtain estimates for the number of their rational points over a number field and ...
Alex Massarenti
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Random Diophantine equations in the primes
Mathematika, Volume 72, Issue 3, July 2026.Abstract We consider equations of the form a1x1k+⋯+asxsk=0$a_{1}x_{1}^{k}+\cdots +a_{s}x_{s}^{k}=0$ where the variables xi$x_{i}$ are all taken to be primes. We define an analogue of the Hasse principle for solubility in the primes (which we call the prime Hasse principle), and prove that, whenever k⩾2$k\geqslant 2$, s⩾3k+2$s\geqslant 3k+2$, this holds
Philippa Holdridge
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Generalized free wreath products and their operator algebras
Journal of the London Mathematical Society, Volume 113, Issue 6, June 2026.Abstract We develop a new approach on free wreath products, generalizing the constructions of Bichon and of Fima‐Pittau. We show stability properties for certain approximation properties such as exactness, Haagerup property, hyperlinearity, and K‐amenability. We study qualitative properties of the associated von Neumann algebra: factoriality, primeness,
Pierre Fima, Arthur Troupel
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Counting 5‐isogenies of elliptic curves over Q$\mathbb {Q}$
Journal of the London Mathematical Society, Volume 113, Issue 5, May 2026.Abstract We show that the number of 5‐isogenies of elliptic curves defined over Q$\mathbb {Q}$ with naive height bounded by H>0$H > 0$ is asymptotic to C5·H1/6(logH)2$C_5\cdot H^{1/6} (\log H)^2$ for some explicitly computable constant C5>0$C_5 > 0$. This settles the asymptotic count of rational points on the genus zero modular curves X0(m)$\mathcal {X}
Santiago Arango‐Piñeros +3 more
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Fortschritte der Physik, Volume 74, Issue 4, April 2026.ABSTRACT In this paper, we continue the development of the Cartan neural networks programme, launched with three previous publications, by focusing on some mathematical foundational aspects that we deem necessary for our next steps forward. The mathematical and conceptual results are diverse and span various mathematical fields, but the inspiring ...
Pietro Fré +4 more
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