no. G10
Théorie des nombres
There are no Carmichael numbers of the form 2 n p+1 with p prime
Alahmadi, Adel1 ; Luca, Florian2, 3, 4 
1 Research Group in Algebraic Structures and its Applications, King Abdulaziz University, Jeddah, Saudi Arabia
2 School of Maths, Wits University, 1 Jan Smuts, Braamfontein 2000, Johannesburg, South Africa
3 Centro de Ciencias Matemáticas, UNAM, Morelia, Mexico
4 Research Group in Algebraic Structures and Applications, King Abdulaziz University, Abdulah Sulayman, Jeddah 22254, Saudi Arabia
Comptes Rendus. Mathématique, Tome 360 (2022) no. G10, pp. 1177-1181.

In this paper, we prove the theorem announced in the title.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.393
Classification : 11A51
Alahmadi, Adel 1 ; Luca, Florian 2, 3, 4

1 Research Group in Algebraic Structures and its Applications, King Abdulaziz University, Jeddah, Saudi Arabia
2 School of Maths, Wits University, 1 Jan Smuts, Braamfontein 2000, Johannesburg, South Africa
3 Centro de Ciencias Matemáticas, UNAM, Morelia, Mexico
4 Research Group in Algebraic Structures and Applications, King Abdulaziz University, Abdulah Sulayman, Jeddah 22254, Saudi Arabia 
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     author = {Alahmadi, Adel and Luca, Florian},
     title = {There are no {Carmichael} numbers of the form $2^np+1$ with $p$ prime},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1177--1181},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {360},
     number = {G10},
     year = {2022},
     doi = {10.5802/crmath.393},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/crmath.393/}
}
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Alahmadi, Adel; Luca, Florian. There are no Carmichael numbers of the form $2^np+1$ with $p$ prime. Comptes Rendus. Mathématique, Tome 360 (2022) no. G10, pp. 1177-1181. doi : 10.5802/crmath.393. http://www.numdam.org/articles/10.5802/crmath.393/

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