We prove that if $f(x)=\sum _{k=0}^{n-1}a_{k}x^{k}$ is a polynomial with no cyclotomic factors whose coefficients satisfy $a_{k}$ ≡ 1 mod 2 for 0 ≤ k < n, then ...

A pair of mathematicians solved a legendary question about the proportion of vertices in a graph with an odd number of connections. “It’s a bit of a surprise, at least for me, that such a combination ...

In this paper, we study the symmetric and the generating functions for odd and even terms of the second-order linear recurrence sequences. we introduce a operator in order to derive a new family of ...