For which $$n\in \mathbb{N}$$, does $$n+1 | \binom{2n}{n}$$ hold? For a polynomial $$p(x) = a_nx^n+\ldots + a_0$$ with integral coefficients, i.e. $$a_i\in \mathbb{Z}$$ for all $$1\leq i\leq n$$ with $$a_n\neq 0$$, if $$p(\frac{r}{s})=0$$ where $$r$$, $$s$$ are coprime integers with $$s\neq 0$$ then show that: $$r|a_0$$ ...

In this article  we shall show that the characteristic polynomial of both $$AB$$ and $$BA$$ are the same, where $$A$$ and $$B$$ are $$n\times n$$ matrices over $$R$$, a ring with unity. Let $$\Phi_T\in R[\lambda]$$ denote the characteristic polynomial of $$T$$. Thus, we intend to show,...

Po-Shen Loh is an associate professor of mathematics at the Carnegie Mellon University. He specializes in probabilistic and extremal combinatorics. He is the founder of Expii which "is a free interactive website, focused on math and science, where students, teachers, tutors, and enthusiasts are encouraged to add...

In this article we see that the automorphism group of biholomorphic functions of the upper half plane and the open unit ball in the complex plane is isomorphic to the second projective special linear group over the field of real numbers. [pdf-embedder url="http://gonitsora.mathematics.website/wp-content/uploads/2016/05/automorphisms-upper-half.pdf"] Click here to download. Image Source...

People have been in an attempt to find roots of polynomials since a very long time. They may not have had a very concrete notion of a polynomial and may have been trying to solve some specific polynomials rather than solving some general polynomials. The...