Page 28 - Numbertheory

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yx gcd(a, b ) = 1
sr
bc ac .1 = ax + by

. c = bs c = ar

c = c ×1 = c (ax + by )
= cax + cby

= bsax + arby

= ab (sx + ry )

. ab c

() gcd(a, b ) = 1
. 48
8 ×12 = 96 12  48 8  48
.a  c
a  bc gcd(a, b ) = 1 ()

yx gcd(a, b ) = 1

.c = acx + bcy c . 1 = ax + by
. a  bc a  ac
. a  (acx + bcy )
.a | c
12  9×8 .( )
gcd(a, b ) = 1

.12 8 12 9

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