German theorem of Sophie

The theorem of Sophie Germain states the following property:

For entire naturalness $n$ strictly larger than 1,

$n^4\; +\; 4~$

is not first.

More generally, the mathematician establishes the following equality:

$n^4\; +\; 4\; m^4\; =\; (n^2\; +\; 2\; m^2\; +\; 2\; mn)\; (n^2\; +\; 2\; m^2\; -\; 2\; mn)\; ~$

One also calls theorem of Sophie Germain the following result:

Either $\backslash ,\; p$ a prime number such as $\backslash ,\; 2p+1$ or also a prime number. Then, there do not exist nonnull entireties $x,\; \backslash ,\; there,\; \backslash ,\; z$, and not multiples of $\backslash ,\; p$, such as $\backslash ,\; x^p\; +\; y^p\; =\; z^p$ (in other words, the first case of (large) the theorem of Fermat is true for such exhibitors).

Random links:

Massimo Di Ioia | Damaras | Santa Croce sull'Arno | Spondylus | First knights of the country of Oc | Kate_Roberts

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