***************
Theorem (133). Let $c$ be a prime, and $P$ a polynomial in $x$,
of degree $m$ and $P$ be a divisor of the binomial x^(c-1) - 1;
there are always m values of $x$, between +c/2 and -c/2, to make
this polynomial divisible by $c$.
Theorem (348). Being proposed the equation (x^n-1)/a = e, where
$a$ is prime, and $n$ divides a-1.
(...)
2nd. If $t$ is a value for $x$, t^m will be too, whatever the
exponent $m$ is.
3rd. If the number $t$ is such that t^(n/v)-1 is not divisible
by $a$, $v$ being a prime divisor of $n$, then the formula
x = t^m will contain all the solutions of the proposed equation,
and they will be 1, t, t^2, ... t^(n-1), or the rest of these
quantities divided by $a$.
***************
On August 25, 1999, Heinz himself admitted about Theorem (348):
> Here primitive roots are characterized.
And for me, (133) is a sufficient existence's proof.
Udai Venedem
http://perso.wanadoo.fr/alta.mathematica/
(new catalogue, and thematic pages - one in particular, on number
theory - in French)