(7) |

Let

^{ ... } |
(8) |

Hence the following properties hold:

- every divisor of
*a*and*b*divides*r*_{k}, *r*_{k}divides*a*and*b*.

(37) -> a:= (4*x-1/2) * (x+2) * (5*x+1) * (1/20*x+1) 4 883 3 333 2 49 (37) x + --- x + --- x + -- x - 1 40 8 20 (38) -> b := (4*x-1/2) * (x+4) * (5*x-1) * (1/20*x+1) 4 947 3 2889 2 127 (38) x + --- x + ---- x - --- x + 2 40 40 5 (39) -> r2 := a rem b 8 3 153 2 557 (39) - - x - --- x + --- x - 3 5 5 20 (40) -> r3 := b rem r2 209 2 33231 209 (40) --- x + ----- x - --- 80 640 32 (41) -> r4 := r2 rem r3 (41) 0

euclideanGcd(a,b) == a:=unitCanonical a b:=unitCanonical b while not zero? b repeat (a,b):= (b,a rem b) b:=unitCanonical b return a

(2) -> a: P := (4*x-1/2) * (x+2) * (5*x+1) * (1/20*x+1) 4 883 3 333 2 49 (2) x + --- x + --- x + -- x - 1 40 8 20 (3) -> b: P := (4*x-1/2) * (x+4) * (5*x-1) * (1/20*x+1) 4 947 3 2889 2 127 (3) x + --- x + ---- x - --- x + 2 40 40 5 (4) -> r2 := unitCanonical(a rem b) 3 153 2 557 15 (4) x + --- x - --- x + -- 8 32 8 (5) -> r3 := unitCanonical(b rem r2) 2 159 5 (5) x + --- x - - 8 2 (6) -> r4 := unitCanonical(r2 rem r3) (6) 0

2004-04-27