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Ternary Diophantine equations of signature (p, p, 3)
In this paper, we develop machinery to solve ternary Diophantine equations of the shape Axn + Byn = Cz3 for various choices of coefficients (A,B, C). As a byproduct of this, we show, if p is prime,Expand
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CvxNet: Learnable Convex Decomposition
TLDR
We introduce a network architecture to represent a family of convex polytopes based on primitive decomposition. Expand
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Periodicity, morphisms, and matrices
TLDR
We apply our methods to a previously unsolved conjecture on iterated morphisms, the decreasing length conjecture: if h + k − gcd(h,k) were replaced by any smaller number, then k ≤ n. Expand
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Generalized Fermat equations: A miscellany
This paper is devoted to the generalized Fermat equation xp + yq = zr, where p, q and r are integers, and x, y and z are nonzero coprime integers. We begin by surveying the exponent triples (p, q,Expand
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Multiplicative functions and k-automatic sequences
Une suite est dite k-automatique si son ne terme peut etre engendre par une machine a etats finis lisant en entree le developpement de n en base k. Nous prouvons que, pour de nombreuses fonctionsExpand
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On the greatest prime factor of some divisibility sequences
Let $P(m)$ denote the greatest prime factor of $m$. For integer $a>1$, M. Ram Murty and S. Wong proved that, under the assumption of the ABC conjecture, $$P(a^n-1)\gg_{\epsilon, a} n^{2-\epsilon}$$Expand
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Modular Abelian Varieties of Odd Modular Degree
In this paper, we will study modular Abelian varieties with odd congruence numbers by examining the cuspidal subgroup of $J_0(N)$. We will show that the conductor of such Abelian varieties must be ofExpand
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An extremal property of Fekete polynomials
The Fekete polynomials are defined as
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Geometry of 'standoffs' in lattice models of the spatial Prisoner's Dilemma and Snowdrift games
The Prisoner’s Dilemma and Snowdrift games are the main theoretical constructs used to study the evolutionary dynamics of cooperation. In large, well-mixed populations, mean-field models predict aExpand
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Fekete-like polynomials
Abstract In 2001, Borwein, Choi, and Yazdani looked at an extremal property of a class of polynomial with ±1 coefficients. Their key result was: Theorem (See Borwein, Choi, Yazdani, 2001.) Let f ( zExpand
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