# Local Maxima of Number of Goldbach Decompositions

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## Contents

## Theorem

Let $\mathbb E$ be the set of even positive integers.

Let $G: \mathbb E \to \N$ be the mapping defined as:

- $\forall n \in \mathbb E: \map G n =$ the number of Goldbach decompositions of $n$.

Then $G$ has local maxima when $n$ is a multiple of $6$.

## Proof

## Historical Note

This theorem is reported by David Wells, in his $1997$ *Curious and Interesting Numbers, 2nd ed.* to have been demonstrated by R.M. Sternheimer, in Volume $24$ of *Journal of Recreational Mathematics*, page $30$, but corroborative evidence is not easily come by.

## Sources

- 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $6$