On the Common Prime Divisors of Polynomials

We inspect those polynomials whose coefficients are integers. We say that an integer m is a divisor of a polynomial P if some value of P is divisible by m. Our main result is that the common divisors of any several polynomials are exactly the divisors of a single polynomial. This is extended to prove that the set of prime numbers for which a system of polynomial equations in multiple variables is solvable is exactly the set of prime divisors of some polynomial in one variable. In addition, we prove results on how often a prime number is a common prime divisor of some polynomials – we prove a tight lower bound for this so-called density, and under additional assumptions give a formula for this density. Our work generalizes previous results, and we propose several ideas for further research.

EcoMe: a reusable, ecological and affordable menstrual hygiene product for developing regions

EcoMe is a reusable, ecological and affordable menstrual protection product aimed for developing regions. The qualities of the menstrual pad are based on an interdisciplinary research. A user survey was conducted in three Asian regions: Mongolia, Azerbaijan and China. From the results, limitations and preferences towards an ideal menstrual product were obtained and further used in the design of the product. Different materials were explored and the decision on using sea sponge as an absorbing material is based on the most important qualities of the material: absorbance, drying time and cleansing. In addition, an informative mobile application was created. The mobile application includes information about topics such as puberty, menstruation and contraception.