Robert J. Betts

collaborators

Showing math.NTShow all

3 papers · 1 filter

math.NT2012

A simple Proof that $r^{k^{2}}$ is an upper Bound on each van der Waerden Number $W (r, k)$ , for each $k$ bounded below by a certain positive real Number $ε$

Robert J. Betts

Here we answer a conjecture by Ron Graham about getting finer upper bounds for van der Waerden numbers in the affirmative, but without the application of double induction or combin…

math.NT2010

A uniformly convergent Series for $ζ (s)$ and closed Formulas, that include Catalan Numbers

Robert J. Betts

There exists an infinite series of ratios by which one can derive the Riemann zeta function $ζ (s)$ from Catalan numbers and central binomial coefficients which appear in the terms…

math.NT2010

Deriving from an Assumption a semistable elliptic Curve for $x_{0}^{k} + y_{0}^{l} = z_{0}^{m}$

Robert J. Betts

With a simple transformation of the three exponents the generalized Fermat equation can be put into the same form as the Fermat equation. When it is rewritten into this new altered…

A simple Proof that rk2 is an upper Bound on each van der Waerden Number W(r,k), for each k bounded below by a certain positive real Number ε

A uniformly convergent Series for ζ(s) and closed Formulas, that include Catalan Numbers

Deriving from an Assumption a semistable elliptic Curve for \(x_{0}^{k} + y_{0}^{l} = z_{0}^{m}\)

A simple Proof that $r^{k^{2}}$ is an upper Bound on each van der Waerden Number $W (r, k)$ , for each $k$ bounded below by a certain positive real Number $ε$

A uniformly convergent Series for $ζ (s)$ and closed Formulas, that include Catalan Numbers