> There seems to be some confusion still in the questions
I do not see any confusion in my questioning, and still William CW be
thanked for the interesting precisions he found in Wussing. It would
help more if he could give the titles of the works, the review or edition
(and not only the year) where Abel and Cauchy gave the said uses of the
term "order".
Then, William writes:
> Second, we have
> **********
> the minimum $r$ such that b^r=1 (mod n).
> **********
> Note that this second idea is never (to my knowledge) called an index.
I can give two counter-examples to this "never":
1) The cause of my research on this topic, Avinoam Mann, who wrote to me:
***the "order" is sometimes referred to in number theory books, especially
older ones, as "index".***
2) Borel himself, in his "Les nombres premiers" (PUF, Paris 1953), p. 63,
after repeating his 1895 phrasing, adds:
************
nous conviendrons de dire aussi que r est l'indice de b
************
Beside the question of the first use of the term "index", can't we find in
Euler this notion of "minimum power" ("exposant minimal") and also the
possibility of expressing any number by a power of a primitive root?
Udai Venedem
venedem@wanadoo.fr
http://perso.wanadoo.fr/alta.mathematica/
(new catalogue, and thematic pages, in French)