> Following Antreas P. Hatzipolakis's forwarded message, I wandered in
> http://vamri.xray.ufl.edu/proths/status.html
> where I found:
> *************
> Proth's Theorem (1878): Let n = k.(2^q)+1 with 2^q > k. If there is an
> integer $a$ such that a^((n-1)/2) = -1 (mod n), then $n$ is prime.
> *************
> It may be interesting to notice that, in his "The/orie des nombres"
> (Paris, Gauthier-Villars, 1891), p. 441, Edouard Lucas claims he stated
> for the first time in 1876 the following (famous) theorem:
> *If a^x = 1 (mod n) for x = n-1 and for no other divisor of (n-1), then
> the number $n$ is prime.*
> of which Proth's is a quite obvious consequence.
(French text by Lucas deleted)
> **************************
> Does anyone know about this question of priority? By the way, who Proth
> was, and where did he publish his (?) theorem?
> Udai Venedem
> venedem@wanadoo.fr
> http://perso.wanadoo.fr/alta.mathematica/
While both theorems are not difficult to prove, I am not sure that Proth's
follows from Lucas'.
Avinoam Mann