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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!

Wolbachia pipientis (Wolbachia) is a maternally inherited endosymbiotic bacterium that infects over 50% of arthropods, including pillbugs, and acts as a reproductive parasite in the host. In the common terrestrial pillbug Armadillidium vulgare (A. vulgare), Wolbachia alters the sex ratio of offspring through a phenomenon called feminization, where genetic males develop into reproductive females. Previous studies have focused on the presence or absence of Wolbachia as a sex ratio distorter in laboratory cultured and natural populations mainly from sites in Europe and Japan. Our three-year study is the first to evaluate the effects of the Wolbachia sex ratio distorter in cultured A. vulgare offspring in North America. We asked whether Wolbachia bacteria feminize A. vulgare isopod male offspring from infected mothers and if this effect can be detected in F1 offspring by comparing the male/female offspring ratios. If so, the F1 offspring ratio should show a higher number of females than males compared to the offspring of uninfected mothers. Over three years, pillbug offspring were cultured from pregnant A. vulgare females and developed into adults. We determined the Wolbachia status of mothers and counted the ratios of male and female F1 progeny to determine feminization effects. In each year sampled, significantly more female offspring were born to Wolbachia-infected mothers than those from uninfected mothers. These ratio differences suggest that the Wolbachia infection status of mothers directly impacts the A. vulgare population through the production of reproductive feminized males, which in turn provides an advantage for further Wolbachia transmission.