Page 29 - Numbertheory

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. gcd a , b  =1 gcd(a, b ) = d ()
d d 

yx gcd(a, b ) = d

d .d = ax + by
.1= a x + b y
. gcd a , b  = 1 ()
d d  dd

. lcm (a,b )  c ()

b c ac

bc ac . m = lcm (a, b )

m = ab . c = by c = ax yx
d
. d = gcd(a, b )
sr

. d = ar + bs

c = cd
m ab

= car +cbs
ab

= c r + c s
   
 b  a
.m c .

nm [RUMO 1995] ( )

lcm (m , n ) + gcd(m , n) = m + n

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