CRPC/Rice University Softlibsoftlib.rice.edu/pub/CRPC-TRs/reports/CRPC-TR96718-S.pdf · ¤1¥§¦...

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0

1

2

3

4

5

6

7

8

9

10

11

gcd(P,Q)

gcd(P,Q)

gcd(P,Q)

0 1

2

3

3

1

0

2 4 5

gcd(P,Q)

Process(2,4):

2−4 = mQ − lP

2+lP = 4+mQ = 10

i.e, process(2,4) is

P=4, Q=6; l=2, m=1

Ordering of the mainD−processes:

D−process.

the 11th main

A�

A�

B

B

C�C

D

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lP+p

(l+1)P+p

(l+2)P+p

(l+3)P+p

mQ+q

a=1

P=2, Q=3: aQ − bP = gcd(P,Q) = 1 => a=1, b=1 and cQ − dP = −1 => c=1, d=2.

lcm(P,Q)=6

lcm(P,Q)=6

(m+1)Q+q (m+2)Q+q

lcmq=2

lcmp=3

D2

D1

D0

D0

D2

D1

B2

B1

c=1

b=1

d=2

B0

B3

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0 50 100 150 200 250 300 350 400 450 50010

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gcd(Pmb,Qnb) <= mb+nb−gcd(mb,nb)gcd(Pmb,Qnb) <= mb+nb

0 50 100 150 200 250 300 350 400 450 5000.85

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