3 papers
math.HO2017
A Proof of Symmetry of the Power Sum Polynomials using a Novel Bernoulli Numbers Identity
Nicholas J. Newsome, Maria S. Nogin, Adnan H. Sabuwala
The problem of finding formulas for sums of powers of natural numbers has been of interest to mathematicians for many centuries. Among these is Faulhaber's well-known formula expre…
math.NT2017
Congruences of Power Sums
Nicholas J. Newsome, Maria S. Nogin, Adnan H. Sabuwala
The following congruence for power sums, , is well known and has many applications: $1^n+2^n +\dots +p^n \equiv\begin{cases} -1 \text{ mod } p, & \text{ if } \ p-1 \ | \ n;…
math.HO2016
It is not a Coincidence! On Curious Patterns in Calculus Optimization Problems
Maria Nogin
In this paper we consider a few Calculus optimization problems in which we notice peculiar patterns. In each of these cases there is a geometric explanation for the pattern showing…