1. , . , ( ), , , , .
. , , , , : .
an = an1 + an 2, bn = bn1 + bn 2.
, a1 = 1 = a2 b1 = 1 = b2, . . . , , , .
76 , . . - , , , , . 10 . , , ?
:
:
1; 1; 2; 3; 5; 8; 13; 21;
an = an1 + an 2, 1 = 2 = 1.
76 = 21 + 21 + 34. (. . )
N N .
a, b , (a; b) a b .
(a; b) a b.
(a; b) N a b.
k ( ) (a; b; c), :
1. (a; b) (b; ) ;
2. (a; b) (b; ) xk, - xk,
xk+1;
3. b .
1.
, k 1.
(a; b; c) k.
1 : (a; b) (b; ) xk.
(a; b) d , (a; d) (d; b) xk-2
xk-1 . :
) d < b ⟹ (d; b; c) k 1;
) d > b ⟹ (a; d; b) k 2.
2 : (a; b) - xk+1 ( ), (b; ) - xk.
d , (a; d) (d; b) xk xk-1.
:
) d < b ⟹ (d; b; c) k 1;
) d > b ⟹ (a; d; b) k 1.
|
|
( )
1, k 1 .
- k.
: N = 76 = 21 + 21 + 34 = 2 xk + xk+1.
( a; b k + 2 , . .
10 ).
: 10 .
3.
, 64 = 65.
8 , .
13 5, . . , 65.
, , . , A, B, C D , , .
, ( ), , 8 , , an. (. ) . , , , . , . . , , ,
.
, 21 34 13 ,
≈ 0,4 , .