Results 51 to 60 of about 321 (189)
Journal of the London Mathematical Society, Volume 113, Issue 5, May 2026.Abstract We survey ideas surrounding the study of the number of integers that can be represented as the sum of three positive cubes. We focus on the early contribution of Davenport using elementary techniques, and the subsequent developments due to Vaughan, which introduced Fourier analysis and mirrored many of the important developments of the Hardy ...
James Maynard
wiley +1 more source
On the exponential Diophantine equation (18m(2 )+1)(x) + (7m(2)-1)(y) = (5m)(z) [PDF]
, 2018 Let m be a positive integer. We show that the exponential Diophantine equation (18m(2) + 1)(x) + (7m(2) - 1)(y) = (5m)(z) has only the positive integer solution (x, y, z) = (1, 1, 2) except for m 23, 47, 63, 87 (mod 120) . For m not equivalent to 0 (mod
ALAN, Murat
core +1 more source
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
The ternary exponential Diophantine equation concerning Pythagorean triplets [PDF]
, 2016 Let r be a positive integer with r > 1, and let m be a positive even integer. Further let a = |V (m, r)|, b = |U(m, r)| and c = m2 + 1, where V (m, r) + U(m, r) √-1 = (m + √-1)r.
Di, H, Wenpeng, Z
core
Multiplication polynomials and relative Manin-Mumford [PDF]
, 2015 After the introduction we prove in chapter 2 that the resultant of the standard multiplication polynomials $A_n,B_n$ of an elliptic curve in the form $y^2 = x^3+ax+b$ is $(16\Delta)^{{n^2(n^2-1) \over 6}}$, where $\Delta=-(4a^3+27b^2)$ is the ...
Schmidt, Harry
core +1 more source
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
Tian’s Conjecture on the Prime Factorization of the Binomial Coefficient
MathematicsTian’s conjecture states that for any fixed distinct prime numbers p1,…,pm, the Diophantine equation n+12=p1α1·p2α2···pmαm in positive integers n,α1,…,αm has at most m solutions.
Zhenbing Zeng +3 more
doaj +1 more source
Jeśmanowicz' conjecture on exponential diophantine equations
Functiones et Approximatio Commentarii Mathematici, 2011 Jeśmanowicz' conjecture is the following statement: If \(a\), \(b\), \(c\) are coprime positive integers such that \(a^2+b^2=c^2\) with even \(b\), then the exponential equation \(a^x+b^y=c^z\) has the only solution \((x,y,z)=(2,2,2)\) in positive integers. This paper contains various new results on this conjecture.
openaire +2 more sources
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 a Diophantine equation of Erdős and Graham [PDF]
, 2020 We study solvability of the Diophantine equation in integers satisfying the conditions and for . The above Diophantine equation (of polynomial-exponential type) was mentioned in the monograph of Erdős and Graham, where several questions were stated. Some
Ulas, Maciej +2 more
core +1 more source