Reducible diophantine systems

On Solving Linear Diophantine Systems Using Generalized Rosser's Algorithm

Compositional Systems over Reducible Networks

In the paper two notions related to local (distributed) computations are identified and discussed. The first one is the notion of reducible graphs. A graph is reducible if it can be reduced to a singleton by successive removing its removable nodes; to decide whether a node is removable or not it is sufficient to inspect its neighborhood, hence the removing procedure is local. The second is the ...

Erdős-turán with a Moving Target, Equidistribution of Roots of Reducible Quadratics, and Diophantine Quadruples

ABSTRACT. A Diophantine m-tuple is a set A of m positive integers such that ab + 1 is a perfect square for every pair a, b of distinct elements of A. We derive an asymptotic formula for the number of Diophantine quadruples whose elements are bounded by x. In doing so, we extend two existing tools in ways that might be of independent interest. The Erdős-Turán inequality bounds the discrepancy be...

Systems of quadratic diophantine inequalities

has a nonzero integer solution for every > 0. If some Qi is rational and is small enough then for x ∈ Zs the inequality |Qi(x)| < is equivalent to the equation Qi(x) = 0. Hence if all forms are rational then for sufficiently small the system (1.1) reduces to a system of equations. In this case W. Schmidt [10] proved the following result. Recall that the real pencil generated by the forms Q1, . ...

On the Quantization of Reducible Gauge Systems

Reducible gauge theories with constraints linear in the momenta are quantized. The equivalence of the reduced phase space quantization, Dirac quantization and BRST quantization is established. The ghosts of ghosts are found to play a crucial role in the equivalence proof. † On leave of absence from Instituto de Astronomı́a y F́ısica del Espacio, C.C.167, Sucursal 28, 1428 Buenos Aires, Argentina,...