Results 61 to 70 of about 2,597 (231)
Definability of complex functions in o‐minimal structures
Journal of the London Mathematical Society, Volume 114, Issue 1, July 2026.Abstract We prove that holomorphic continuations of functions in the classes an∗$\mathbf {an}^*$ and G$\mathcal {G}$ are definable in the o‐minimal structures Ran∗$\mathbb {R}_{\operatorname{an}^*}$ and RG$\mathbb {R}_{\mathcal {G}}$, respectively. More specifically, we give complex domains on which the holomorphic continuations are definable and show ...
Adele Padgett, Patrick Speissegger
wiley +1 more source
, 2010 In the first chapter we have given some definations, theorems, lemmas on Elementary Number Theory. This brief discussion is useful for next discussion on the main topic.
Strnadová, Pavlína, Panda, Sagar
core
A Binomial Diophantine Equation [PDF]
, 1995 We answer a question of Richard K. Guy, in proving that i 21 2 j = i 10 4 j = 210 is the largest solution of the binomial diophantine equation i n 2 j = i m 4 j . 1 Introduction In [G, Section D3], Richard K. Guy asks for the existence
B.M.M. de Weger +2 more
core +1 more source
The diophantine equation x2+3m=yn
International Journal of Mathematics and Mathematical Sciences, 1998 The object ofthis paper is to prove the following.
S. Akhtar Arif, Fadwa S. Abu Muriefah
doaj +1 more source
Diophantine equations in partitions [PDF]
Mathematics of Computation, 1984 Given positive integers r 1
openaire +1 more source
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
wiley +1 more source
Unification and equation solving in nilpotent groups and monoids [PDF]
, 1991 Unification and equation solving have been considered for groups [44], semigroups [43], abelian groups [39] and abelian semigroups [25], [33], [68], [69]. In this thesis we consider partially commutative groups and monoids. Nilpotency provides us with a
Burke, Edmund Kieran, Burke, E.K
core
New results on embeddings of self‐similar sets via renormalization
Proceedings of the London Mathematical Society, Volume 133, Issue 1, July 2026.Abstract For self‐similar sets X,Y⊆R$X,Y\subseteq \mathbb {R}$, we obtain new results toward the affine embeddings conjecture of Feng–Huang–Rao (2014), and the equivalent weak intersections conjecture. We show that the conjecture holds when the defining maps of X,Y$X,Y$ have algebraic contraction ratios, and also for arbitrary Y$Y$ when the maps ...
Amir Algom, Michael Hochman, Meng Wu
wiley +1 more source
A Diophantine equation appearing in Diophantine approximation [PDF]
, 2001 All Diophantine equations ax2 + by2 + cz2 = 1 + dxyz, with a, b, c, d ∈ N and a|d, b|d, c|d, having solutions (x, y, z) ∈ N3 are determined. One particular equation of this type 2x2 + 2y2 + 3z2 = 1 + 6xyz appeared recently in connection with the ...
Schmidt, Asmus L., Jin, Yuan
core +1 more source
The Exponential Diophantine Equation 4m2+1x+5m2-1y=(3m)z
Abstract and Applied Analysis, 2014 Let m be a positive integer. In this paper, using some properties of exponential diophantine equations and some results on the existence of primitive divisors of Lucas numbers, we prove that if m>90 and 3|m, then the equation 4m2+1x + 5m2-1y=(3m)z has ...
Juanli Su, Xiaoxue Li
doaj +1 more source