Page 51 - Numbertheory

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a(a + 2) ( ) lcm (a,a + 2) a ()
2 1( ) a + 2( )
a(a + 2) ( )

. gcd(a, a + 2) = 1 a :( )

. lcm (a, a + 2) = a(a + 2) = a(a + 2)

1

gcd(m , c ) m |b gcd(b , c ) = 1 ()

1() b( ) m( ) c ()

d  c .d = gcd(m , c ) :( )

.d = gcd(b ,c ) = 1 . d b m b .d m

:

sr gcd(b , c ) = 1

. b = mk m |b . rb + sc = 1
. (rk )m + sc = 1
. gcd(m , c ) = 1

n( )
n 2 = 3k + 2 ( )
n 2 = 3k +1 n 2 = 3k ( ) n 2 = 4k + 2 ( )
n 2 = 4k +1 n 2 = 4k ( )

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