a b, a .
b a, q, a=bq.
, , .
:
9 3, 9: 3 = 3;
9 4, 9: 4 = 2 1/4
O (1) : 2: 1 = 2; 4: 1 = 4; 11: 1 = 11 . . .
: 12: 6 =2; .
. : , .
́ ́ ( ) , . , x , 1 1 x. , 5 , 6 , , 1 6, 2 3.
, , . , : ( ), ( ) ( ). .
, , 1. :
14 25 .
15 25 ( 5).
6, 8, 9 , .
:
a b , :
a b ;
y , ax+by=1 ( ).
() .
a bc, a b, a c.
, .
. , . .
ü 2, 2 . : 52 2. 2 2 (2: 2 = 1).
11 2. 1 2.
ü 3, 3. : 153 3. : 1 + 5 + 3 = 9 3 (9: 3 = 3). 11 3. : 1 + 1 = 2 3.
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ü 5, 5 0. : 155 5. 5. 61 5. 1.
ü 9, 9. : 486 9. : 4 + 8 + 6 = 18 9 (18: 9 = 2)
55 9. : 5 + 5 = 10 9.
16) . : (a, b). (a, b).
, . , 36, 60, 2, 3 6.
() a b , a b .
() :
ü ;
. , . .
. 28 6
.
28 = 2 2 7 64 = 2 2 2 2 2 2
;
(28; 64) = 2 2 = 4 : (28; 64) = 4
, . 72 64. :
72 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
64 1, 2, 4, 8, 16, 32, 64
, 72 64 1, 2, 4 8. 8. 72 64.
18) . : (a, b), , . (a, b).
, .
a , a .
8 ( , 8 ): 16, 24, 32
, a , . .
() , .
ü .
, , .
a ʻ.
(a) = {...,...} . 6 8. (6) = {12, 18, 24, 30,...} (8) = {8, 16, 24, 32,...} (6, 8) = 24
ü . . (a, b)=ab:(a, b). .
126 70. a=126, b=70. , (a, b)=ab:(a, b). , 70 126, .
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(126, 70), : 126=701+56, 70=561+14, 56=144, , (126, 70)=14.
: (126, 70)=12670:(126, 70)=12670:14=630.