Results 41 to 50 of about 1,519,699 (118)
Random Diophantine equations in the primes II
Journal of the London Mathematical Society, Volume 113, Issue 5, May 2026.Abstract Let d⩾2$d\geqslant 2$ and n⩾d$n\geqslant d$ with (d,n)∉{(2,2),(3,3)}$(d,n)\notin \lbrace (2,2),(3,3)\rbrace$. We consider homogeneous Diophantine equations of degree d$d$ in n+1$n+1$ variables and whether they have solutions in the primes.
Philippa Holdridge
wiley +1 more source
Ternary Diophantine Equations via Galois Representations and Modular Forms
, 2004 In this paper, we develop techniques for solving ternary Diophantine equations of the shape Axn + Byn = Cz2, based upon the theory of Galois representations and modular forms.
Michael A. Bennett, Chris M. Skinner
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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
wiley +1 more source
Diophantine equations involving factorials [PDF]
, 2017 We study the Diophantine equations $(k!)^n -k^n = (n!)^k-n^k$ and $(k!)^n +k^n = (n!)^k +n^k,$ where $k$ and $n$ are positive integers. We show that the first one holds if and only if $k=n$ or $(k,n)=(1,2),(2,1)$ and that the second one holds if and only
Gnatowski, Maciej +2 more
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Solving the n $n$‐Player Tullock Contest
Journal of Public Economic Theory, Volume 28, Issue 2, April 2026.ABSTRACT The n $n$‐player Tullock contest with complete information is known to admit explicit solutions in special cases, such as (i) homogeneous valuations, (ii) constant returns, and (iii) two contestants. But can the model be solved more generally?
Christian Ewerhart
wiley +1 more source
On the exponential diophantine equations of degree three [PDF]
, 2019 Diophantine equation is known as a polynomial equation with two or more unknowns which only integral solutions are sought. This paper concentrates on finding an integral solution to the exponential Diophantine equation of degree three.
Sapar, Siti Hasana +1 more
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Exploring Zilber's conjecture on atypical intersections in tori and beyond
Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.Abstract In 2002 Zilber, motivated by some model‐theoretical study of the formal theory of exponentiation, proposed a conjecture on ‘atypical’ intersections of subvarieties in tori. This conjecture, raised also independently by Bombieri, Masser and Zannier, and its generalization in the more general setting of mixed Shimura varieties due to Pink, led ...
Laura Capuano
wiley +1 more source
Diophantine equations in positive characteristic [PDF]
, 2019 In this thesis three different topics in number theory are studied. The first part deals with exponential Diophantine equations in positive characteristic. In the second part various statistical properties of class groups are proven.
Koymans, P.H.
core
The Number of Partitions of a Set and Superelliptic Diophantine Equations [PDF]
, 2020 In this chapter we start by presenting some key results concerning the number of ordered k-partitions of multisets with equal sums. For these we give generating functions, recurrences and numerical examples.
Dorin Andrica +5 more
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Distribution of integer points on determinant surfaces and a mod‐p analogue
Mathematika, Volume 72, Issue 2, April 2026.Abstract We establish an asymptotic formula for counting integer solutions with smooth weights to an equation of the form xy−zw=r$xy-zw=r$, where r$r$ is a non‐zero integer, with an explicit main term and a strong bound on the error term in terms of the size of the variables x,y,z,w$x, y, z, w$ as well as of r$r$.
Satadal Ganguly, Rachita Guria
wiley +1 more source