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December 26, 2004

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(1)

   



 º º

December 26, 2004

    

(2)

1

 

1

1.1 . . . . 1

1.2 495

 

. . . . 1

1.3



495

  

. . . . 1

(3)

1

 

1.1



  



 

1 2 3 4 5

     DZ

DZ 

N

   DZ 



N

 

N

  

1.2 495



     



207

 

720

 

027

   

 

207

 



207 → 720 − 027 = 693 → 963 − 369 = 594 →

954 − 459 = 495 → 954 − 459 = 495 →



495.

     

1.3

 

495

  

  

3

 

N



7, 13 = 7 + 6



20 = 7 + 6 + 7



   

N

  

N = 7, 7 + 6 = 13, 7 + 6 + 7 = 20, 7 + 6 + 7 + 6 = 26, · · · .

 

a 1 = 7, a 2 = 7 + 6 = 13, a 3 = 7 + 6 + 7 = 20, · · ·





N = a n+2

  

a n+1



a n

  

  

a 1 = 7



a 2 = 13

  



495

    

abc(a ≥ b ≥ c, a = c),



a b c → abc − cba = a − c − 1 9 10 + c − a.



(a − c − 1) + (10 + c − a) = 9,



990, 891, 782, 693, 594

 

 

990 → 990 − 099 = 891 → 981 − 189 = 792

→ 972 − 279 = 693 → 963 − 369 = 594 → 954 − 459 = 495

(4)







1.1

 

1, 2, 3, 4, 5



1, 2, 3.

 



1.2

 

1, 2, 3, 4, 5



1, 2, 3, 4, 5, 6, 7.

 



1.3

 

1, 2, 3, 4, 5



1, 2, 3, 4, 5, 6, 7, 8, 9.

 



1.4

  DZÆ

  

   

 



1.5

   

   

 DZ      DZ

! "  

 

 

1, 2, 3, 4, 5



1, 2, 3, · · · , n

 DZ

  

w i (w 0 = 0)



n + 1 = 2 2p (2q + 1)



w i+1 = w i + (n + 1).

    

 



10

#$

7

#$

3

#$ 

10

#$ %

%  & ' #$% 

 ' 

(5)

3 7 10



    

"

 !





(

 

8 × 6

 

(8, 6)



)" "  

(8, 6)

 

   "   "  

    "   "   

(1)

 "   

(2)

 "  

(3)

 "   

 "  *   

DZ+,  

8 × 

    

"

  



 

 - DZ

 

a = {a 1 , a 2 , · · · , a n }



n



a i ∈ {1, −1}

  

 

b = {b 1 , b 2 , · · · , b n }



⎧ ⎪

⎪ ⎩

a i+n = a i , b k =  n

i=1

a i · a i+k .

(6)

 

a = {1, 1, 1, −1}



b = {0, 0, 0, 4};

 

a = {−1, −1, −1, 1}



b = {0, 0, 0, 4}.

 

b = {b 1 , b 2 , · · · , b n }



b 1 = b 2 = b 3 = · · · = b n−1 = 0; b n = n



n



a = {a 1 , a 2 , · · · , a n }



n

  

a = {1, 1, 1, −1}, {−1, −1, −1, 1}



4

  .     DZ  DZ#  / 

DZ    0 

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