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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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Beeing sustainable: Honey as a bioindicator for pollution

Donnellan et al. | Oct 06, 2021

Beeing sustainable: Honey as a bioindicator for pollution

In this study, Donnellan and colleagues investigated how environmental pollution may be affecting honey samples from Chicago apiaries. They found no significant correlation between heavy metal concentration in honey to distance from local industries, suggesting a minimal effect of proximity to industrial pollution on honey contamination.

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