December 20, 2005



December 20, 2005



105

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 DZ

   


  










121

^          

 

 

 
      

     



  !

25%



12

! 

1 × 12, 2 × 6, 3 × 4

   !!

12 − 1 = 11, 6 − 2 = 4, 4 − 3 = 1.



3 × 4

 ! 

3 × 4



12

 !!

F 12 = ³ ₄

^

24

^

1 × 24, 2 × 12, 3 × 8, 4 × 6

" !

4 × 6

 

4 × 6

^

24

^

!

F 24 = ⁴ ₆ = ² ₃

^


#$  

n

^{ !}

p×q(p ≤ q)

^

 !

F n 

^

F n = ^p _q

^

1-1.

^

18

^{ !!}

F 18

^

1-2.

^

48

^{ !!}

F 48

^

1-3.

^!

F 221

^

1-4.

^!

F 2 ⁹⁹

^

1-5.

^{ }

n

^

F n = 1

^

!

50%

 %&  %&'

 "(

 




2

^

3

^

4

^

128

^

 


25 × 35






2

^





3

^

4

^

8

^

12

^

16

^

20

 ) *

+

 

%&

 

,

500





 !

2

^



1000

^

2

^

2 3 4 8 12 16 20

Þ

25 × 35 25 × 17 ¹ ₂ 25 × 11 ² ₃ 11 ¹ ₂ × 17 ¹ ₂

11 ¹ ₂ × 8 ³ ₄ 8 ¹ ₃ × 8 ³ ₄

6 ¹ ₄ × 8 ³ ₄ 6 ¹ ₄ × 7

2-1. a) 64

%&

32

%&

b) 25

%&

18

%&

c)

 ! %&




d)

 -
-

12 .5

^{. }

a) 64

"(%&

24

"(%&

b) 7

"(%&

90

"(%&

c) 96

"(%&

DZ

25%

 # #  # 

+ 1   2

3 


 4

*
 + 4$ 
+



π = 3.141592653 √

2 = 1.4142135

Ì
 

3-1.

  +/

3-2.

^DZ4 

4 
+

+ 

1-1.

^

18

^

1 × 18, 2 × 9, 3 × 6

 !

3 × 6

 

3 × 6

^

18

^{ !}

F 18 = ³ ₆ = ¹ ₂

^

1-2.

^

48

^

1 × 48, 2 × 24, 3 × 16, 4 × 12, 6 × 8

5 !

6 × 8

 

6 × 8

^

48

^{ !}

F 48 = ⁶ ₈ = ³ ₄

^

1-3.

^

221 = 13 × 17

^

221

^

1 × 221, 13 × 17

!

13 × 17

 

13 × 17

^

221

^{ !}

F 221 = ¹³ ₁₇

^

1-4.

^

2 ⁹⁹

^

1 × 2 ⁹⁹ , 2 ¹ × 2 ⁹⁸ , 2 ² × 2 ⁹⁷ , · · · 2 ⁴⁴ × 2 ⁴⁵

45

^!

2 ⁴⁴ ×2 ⁴⁵

 

2 ⁴⁴ ×2 ⁴⁵



2 ⁹⁹

^{ !}

F 2 ⁹⁹ = ² ₂ ⁴⁴ ₄₅ = ¹ ₂

^

1-5. p × q(p ≤ q) n F = 1

b) 25 = 5 × 5

%&

25

5 × 35

5 = 5 × 7,



18 = 3 × 6

%&

25

3 × 35

6 = 8 1

3 × 5 5 6 .

c)

^

p × q

^

n

^{ !}

n

%&

25

p × 35 q ,



25

^

p

^

q

^

q

^

 

d)

^{
 }

25 × 35

12 .5 = 70

--

70

^

e)

^

70 = 7 × 10

^{ -}

25

7 × 35

10 = 3 4

7 × 3 1 2 .

f)

^

25

^

5 × 7

^

32

^

4 .375 × 6.25

^

5 > 4.375, 7 > 6.25

^

25

^

Æ!

32

^

g)

^{ }

n = p × q

1 ≤ p ≤ q

^

pq ≤ 128

^



25 p × ³⁵ _q

^{ }

1 .2 = 6 5 =

25 p 35 q

= 5 q

7 p

1 .2 = 6 5 =

35 q 25 p

= 7 p 5 q .



42 p = 25q

7 p = 6q

^



42 p = 25q

^

42 |q, 25|p

^

42 · · · 25|pq

^



pq ≤ 128

^7

7 p = 6q

^

pq ≤ 128

^

p = 6, q = 7

^{ }

6 × 7 = 42

^

2-2. a) 64 = 8 × 8

"(%&

31

8 × 43

8 = 3 7

8 × 5 3 8 ; 24 = 4 × 6

"(%&

31

4 × 43

6 = 7 3

4 × 7 1 6 . b) 7 = 1 × 7

"(%&

31

1 × 43

7 = 31 × 6 1 7 ; 90 = 9 × 10

"(%&

31

9 × 43

10 = 3 4

9 × 4 3 10 . c) 96 = 8 × 12

"(%&

31

8 × 43

12 = 3 7

8 × 3 7 12 .

3-1.

^!

x

^

y

^
+

^2x _y

^

+

x y

^6

2 x y = y

x ⇒
y x

 ₂

= 2 .

 #+

√ 2

^

3-2.