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Old 2022-05-25, 09:17   #4
Dobri
 
"Καλός"
May 2018

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Quote:
Originally Posted by Tomazio View Post
How can I prove that if p=3 (mod 4) is a Sophie Germain prime then the Mersenne number 2^p-1 is composite?
Thanks in advance.
For the first known proof, see the following manuscript:
Joseph Louis de Lagrange, Recherches d'arithmétique (1775), pp. 695-795 (in French).
Available: <https://gallica.bnf.fr/ark:/12148/bpt6k229222d/f696#>.

See Lemme III in page 778 and also 49. Scolie I in page 794.
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