We give new proofs of theorems on alternating subsets of integers by means of bijective transformations. It is shown that all known results are consequences of a simple result on the residue class of ...

Recently S. D. Cohen resolved a conjecture of Chowla and Zassenhaus (1968) in the affirmative by showing that, if f(x) and g(x) are integral polynomials of degree n ≥ 2 and p is a prime exceeding (n2 ...

The major challenge when working with permutations is that the factorial function gets very, very large very, very quickly. The BigInteger data type was introduced in the .NET Framework 4.0; it ...

The more ideas and possible mixes and matches a law department manager has available to choose from, the more permutations there are. Obvious, yes, but what are the mathematics? Let's consider an ...