Page 38 - Numbertheory
P. 38
@ @@Hßìÿa@ö§aI@†a‡Èÿa@óî‹Åä@
yx ()
x +y
30 36
. 1 ( ) 1 ( ) 1 ( ) 1 ()
180 90 36 30
lcm (a,a + 2) a ()
a(a + 2) ( ) a(a + 2) ( ) 1( ) a + 2( )
2
gcd(m , c ) m |b gcd(b , c ) = 1 ()
1( ) b( ) m( ) c ()
n ()
n 2 = 3k +1 n 2 = 3k ( ) n 2 = 3k + 2 ( )
n 2 = 4k +1 n2 = 4k ( )
n 2 = 4k + 2 ( )
[AHSME 1951]( )
n n3 −n
6( ) 4( ) 3( ) 2 ()
abcabc [AHSME 1951] ( )
101 ( ) 1001 ( ) 13 11 ( ) 11 7 ( )
1417 1059 [AHSME 1976] ( )
d −r r d 2312
23 ( ) 19 ( ) 17 ( ) 15 ( )
٢٥