A Curious Strong Resemblance between the Goldbach Conjecture and Fermat Last Assertion

Abstract

The Goldbach conjecture (see [2] or [3] or [4]) states that every even integer $e\geq 4$ is of the form $e=p+q$, where ($p,q$) is a couple of prime(s). The Fermat last assertion [solved by A. Wiles (see [1])] stipulates that when $n$ is an integer $\geq 3$, the equation $x^{n}+y^{n}=z^{n}$ has not solution in integers $\geq 1$. In this paper, via two simple Theorems, we present a curious strong resemblance between the Goldbach conjecture and the Fermat last assertion.