Réponses

2014-09-24T18:20:49+02:00
A. a = 462 ; b = 65 ; a - b = 397 donc PGCD(462,65) = PGCD(65,397)
a = 397 ; b = 65 ; a - b = 332 donc PGCD(397,65) = PGCD(65,332)
a = 332 ; b = 65 ; a - b = 267 donc PGCD(332,65) = PGCD(65,267)
a = 267 ; b = 65 ; a - b = 202 donc PGCD(267,65) = PGCD(65,202)
a = 202 ; b = 65 ; a - b = 137 donc PGCD(202,65) = PGCD(65,137)
a = 137 ; b = 65 ; a - b = 72 donc PGCD(137,65) = PGCD(65,72)
a = 72 ; b = 65 ; a - b = 7 donc PGCD(72,65) = PGCD(65,7)
a = 65 ; b = 7 ; a - b = 58 donc PGCD(65,7) = PGCD(7,58)
a = 58 ; b = 7 ; a - b = 51 donc PGCD(58,7) = PGCD(7,51)
a = 51 ; b = 7 ; a - b = 44 donc PGCD(51,7) = PGCD(7,44)
a = 44 ; b = 7 ; a - b = 37 donc PGCD(44,7) = PGCD(7,37)
a = 37 ; b = 7 ; a - b = 30 donc PGCD(37,7) = PGCD(7,30)
a = 30 ; b = 7 ; a - b = 23 donc PGCD(30,7) = PGCD(7,23)
a = 23 ; b = 7 ; a - b = 16 donc PGCD(23,7) = PGCD(7,16)
a = 16 ; b = 7 ; a - b = 9 donc PGCD(16,7) = PGCD(7,9)
a = 9 ; b = 7 ; a - b = 2 donc PGCD(9,7) = PGCD(7,2)
a = 7 ; b = 2 ; a - b = 5 donc PGCD(7,2) = PGCD(2,5)
a = 5 ; b = 2 ; a - b = 3 donc PGCD(5,2) = PGCD(2,3)
a = 3 ; b = 2 ; a - b = 1 donc PGCD(3,2) = PGCD(2,1)
a = 2 ; b = 1 ; a - b = 1 donc PGCD(2,1) = PGCD(1,1)

On en conclut que PGCD(462,65) = 1 en 20 étapes.