Various assays of classical PEG-assisted transformation as well as electrotransformation of Streptomyces parvulus IMET41380 and Streptomyces vinaceus NCIB8852 are described. Contrary to the so far… (More)

Sometimes the proof of the first two equivalences is called Weyl’s Criterion. The proof can be found in numerous books and, in fact, can be found in Michael Filaseta’s class notes for Transcendental… (More)

It is known that there are infinitely many Sierpiński numbers and Riesel numbers in the sequences of triangular numbers, hexagonal numbers, pentagonal numbers, and many other polygonal sequences. Let… (More)

1 Waring’s Problem Problem 1. (Waring’s) For every natural number k ≥ 2 there exists a positive integer s such that every natural number is the sum of at most s k powers of natural number (for… (More)

DIOPHANTINE EQUATIONS INVOLVING ARITHMETIC FUNCTIONS OF FACTORIALS Daniel M. Baczkowski We examine and classify the solutions to certain Diophantine equations involving factorials and some well known… (More)