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Let p, c be distinct odd primes, and l \ge 2 an integer. We find sufficient conditions for the Diophantine equation cy^l=(x^p-1)/(x-1) not to have integer solutions.
Counting the number of solutions to the Erdos-Straus equation on unit fractions
the Erdos-Straus equation unit fractions Number Theory
2011/8/25
Abstract: For any positive integer $n$, let $f(n)$ denote the number of solutions to the Diophantine equation $\frac{4}{n} = \frac{1}{x} + \frac{1}{y} + \frac{1}{z}$ with $x,y,z$ positive integers. Th...
A Fubute Volume Method for the Multi Subband Boltzmann Equation with Realistic 2D Scattering in DG MOSFETs
Double gate MOSFET Multi subband Boltzmann transport equation 2D electron gas deterministic solver
2015/5/6
We propose a deterministic solver for the time-dependent multi-subband Boltzmann transport equation (MSBTE) for the two dimensional electron gas. The MSBTE consists of a set of Boltzmann transport equ...