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# answer61 - 6101 AB yB 1504 1 b < a 2008 B x = a 2 b 2 =(a...

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E @ » L R » * A B 1, 2, 3, …, 2008, B B 1 2 , 2 2 , 3 2 , …, 2008 2 , A B xB B B B yB x + y B B x A B ? , 1504 , N x + y = a 2 , y = b 2 , 2008 1 < a b B 2008 ) )( ( 2 2 - + = - = b a b a b a x B a + bB aB b N 2 ) ( + - + b a b a B (1), aB b =1, a + b 2007 3 + b a B a + b B 3, 5, 7, …, 2007, 1003 x B 1003 , (2), aB b =2, a + b N 1004 4 + b a B a + b B 4, 6, 8, …, 1004, 501 x B 8, 12, 16, …, 2008 , 501 , (3) x B aB b =, a + b =, 3 2 2 + - = b a b a x B (1), , aB b =, a + b =, ) )( ( 2 2 b a b a b a x - + = - = 4 2 - b a B 4 + b a B 8 x B (2), N x B 1003+501=1504 , 13 7 7' ' ' ³ p » ³E 8 = n 8 2 , , a , b , c N c b a b c b a c a c b a c b + + + + + + + + + - 2 4 2 2 2 2 a a , b , c B ? , 2 2 1 + - = - = c b c a ) 1 2 ( , , 1. a + b +2 c = xB a +2 b + c = yB a + b + c = zB x , y , z B a = – x y +3 z , b = y z , c = x zB 2 b –2 c = 2( y x ) , 2 a +4 c = 2( x y + z ) , b = y zB 6101 6102

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c b a b c b a c a c b a c b + + + + + + + + + - 2 4 2 2 2 2 = z z y y z y x x x y - + + - + - ) ( 2 ) ( 2 = 5 ) 2 ( ) 2 2 ( - + + + z y y z y x x y 2. 5 ) 2 ( ) 2 2 ( - + + + z y y z y x x y 1 2 2 5 2 2 4 2 - = - + y x x y 2 2 = z y y z = 2 , x = yB 2 z = y B + + = + + + + = + + c b a c b a c b a c b a 2 ) ( 2 2 2 , = - = c b c a ) 1 2 ( 2 2 1 + - xd a , b , c A c = 8 1 A - = - + - - = - + - - = - + - - = - + - 14 8 2 2 4 4 4 4 3 3 3 3 2 2 2 2 w z y x w z y x w z y x w z y x S ( x , y , z , w ) ? (1, 0, –1, 2) , (–1, 2, 1, 0) , (1, 2, –1, 0) , (–1, 0, 1, 2) [, 1] 1. - = - + - - = - + - - = - + - - = - + - ) 4 .... ( 14 ) 3 ...( 8 ) 2 ...( 2 ) 1 ...( 2 4 4 4 4 3 3 3 3 2 2 2 2 w z y x w z y x w z y x w z y x ) 1 ( ) 2 ( - ( x 2 x )–( y 2 y )+( z 2 z )–( w
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answer61 - 6101 AB yB 1504 1 b < a 2008 B x = a 2 b 2 =(a...

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