Results 21 to 30 of about 892 (168)
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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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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The Mathematical Gazette, 1964 In this note we prove the following Theorem pertaining to Format’s Last Theorem.
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Current Developments in Mathematics, 1995 The authors would like to give special thanks to N. Boston, K. Buzzard, and B. Conrad for providing so much valuable feedback on earlier versions of this paper. They are also grateful to A. Agboola, M. Bertolini, B. Edixhoven, J. Fearnley, R. Gross, L. Guo, F. Jarvis, H. Kisilevsky, E. Liverance, J. Manoharmayum, K. Ribet, D. Rohrlich, M.
H. Darmon, F. Diamond, R. Taylor
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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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Gunderson’s function in Fermat’s last theorem [PDF]
Mathematics of Computation, 1981 We study Gunderson’s function which gives a bound on the first case of Fermat’s last theorem, assuming that the generalized Wieferich criterion is valid for the first n prime bases. We note two unexpected phenomena.
Shanks, Daniel, Williams, H. C.
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Note on Fermat's Last Theorem [PDF]
Transactions of the American Mathematical Society, 1914 for each factor r of x, in case x + O ( mod p ), and for each factor r of X2 _ y2 s in case X2 _ y2 iS prime to p. By applying this theorem, Furtwangler deduces the criterion of Wieferich q (2) 0 (mod p) and the criterion of Mirimanoff q (3) _ O (mod p) for the solution of (1) in integers prime to p.
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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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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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