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# 19 - 901901 100a p m 7 W bc ` a p m a p m p n p n 100 9 a m...

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901901
100 ˜a± - ‹+ €m p ª*À ƒ » 1 2 3 è n p ”* 7 ”@ [ÿEG W •¼ 50 `± - ‹+ 3 4 5 a b c a b cW `±- ‹+ 5 cèn p ª ˜a± - ‹+ €m p ª*À ƒ c ˜a± - ‹+ €m p ª*À ƒ » a b cèn p ª* èn p ª èn p ª 100 9 1,2,3 x , y, z 9 x+y+z =1009 m p ª*À 3,4,5 9 a , b , c y m p ª*À 3,4,5 9 a’ , b’ , c’y y a+b = x a’+b’ = x y a+c = y a’+c’ = y y b+c = z b’+c’ = z y a+b+c =50 a’+b’+c’ =50 9 a+z =50= a’+z b+y =50= b’ + y a = a’y b=b’y c=c’ c+x =50= c’+x B ß& ‹+ y [ÿE [email protected] y Z [ÿE 9 2 K •¼ 9 9

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901902
p xyzw xyzw xyzw xyzw p q 23 23 123 . 0 23 1 . 0 10 = = q x y y y z y w p y 9999990 1 123 10 - = xyzw p q 10 p (123 xyzw - 1)= q ×9999990 p (123 xyzw - 1)= q ×3 3 ×7×11×13×37 p =139 q =16 A p y 999999 9 9 p =13 9 9 p =13 9 12 4.5 < 3 9 9 9 9 9 9 9 9 9 9 9 9 9

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901903 (1) 9 n 1 4 + k 1,5,9,…øeZ ´ª * n øeZ ´ª 1 a y 2 a y 3 a + n a y n n a a a a a a a a 3 2 1 3 2 1 = + + + + (2) 9 n 1 a y 2 a y 3 a + n a y n n a a a a a a a a 3 2 1 3 2 1 = + + + + n 1 4 + k f´ª f´ª (1)9 a 1 = a 2 = = a n - 1 =19 a n - 1 =39 a n = 2 k +1 9 a
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19 - 901901 100a p m 7 W bc ` a p m a p m p n p n 100 9 a m...

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