 
Summary: Computing 38, 369=372 (1987) Computing
9 by SpringerVerlag1987
A Simple Proof of the Validity of the Reduced prs Algorithm
A. G. Akritas, Lawrence, Kansas
Received November 11, 1986; revised February 23, 1987
Abstract  Zusammenfassung
A Simple Proof of the Validity of the Reduced prs Algorithm. Given two univariate polynomials with
integer coefficients, it has been rediscovered [2] that the reduced polynomial remainder sequence (prs)
algorithm can be used mainly to compute over the integers the members of a normal prs, keeping under
control the coefficient growth and avoiding greatest common divisor (gcd) computations of the coefficients.
The validity proof of this algorithm as presented in the current literature [2] is very involved and has
obscured simple divisibility properties. In this note, we present Sylvester's theorem of 1853 [4] which
makes these simple divisibility properties clear for normal prs's. The proof presented here is a
modification of Sylvester's original proof.
AMS Subject Classifications: 68A15, 6803.
Key words: Polynomial greatest common divisor, polynomial remainder sequence, Sylvester's theorem
(1853).
Ein einfacher Beweis der Giiitigkeit des reduzierten PolynomRestSequenzAlgorithmus. Ftir zwei
gegebene Polynome in einer Variablen und mit ganzzahligen Koeff'Lzienten wurde wiederentdeckt [2],
dab der reduzierte prsAlgorithmus haupts~chlich verwendet werden kann, um die Elemente einer
