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An Analysis of the Density and Patterns of the Solutions of Diophantine Equations of the Third Power

Grewal et al. | Oct 05, 2020

An Analysis of the Density and Patterns of the Solutions of Diophantine Equations of the Third Power

In this study, the authors sought to find out how many mathematical solutions there were to the Indian mathematician Ramanujan's formula, which is a3 + b3 + c3 = d3, and also quantify the densities its solutions. They wrote their own computer program to do so and kept values of a, b, and c less than 10,000. While conducting the analysis, they were also looking for perfect power taxicab numbers and their frequency. They were able to find solutions and densities for the equation. Additionally, while they found that most perfect cube taxicab numbers had a frequency of 2 or 3, they also found on number with a frequency of 42!

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Bacterial Richness of Soil Samples from Southern New Hampshire

Chalasani et al. | Sep 21, 2016

Bacterial Richness of Soil Samples from Southern New Hampshire

Advancement in DNA sequencing technology has greatly increased our understanding about the role of bacteria in soil. The authors of this study examine the microbial content of soil samples taken from three locations in southern New Hampshire with varying pH and plant composition.

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