. , (p Î N, > 1).
. , , - . : , 2, 3,..., n, n +1, ....
, . n, n ≤ m < pn +1.
1) n ≤ m, n . : = n an + mn. an mn , 0 < an < 0 ≤ n < n.
2) n pn -1 . : mn = n -1 an -1 + mn -1, 0 ≤ a -1 < 0 ≤ -1 < -1.
3) -1 -2 . :
mn -1 = n -2 an -2 + mn -2; 0 ≤ an -2< 0 ≤ n -2< n -2.
.
n) :
m 2= a 1+ m 1, 0 ≤ a 1< 0 ≤ 1 < . 1 = 0.
, 1), 2), 3), , n) : = an n + an -1 n -1 +... + a 1 p + 0, 0 ≤ ai < (i = 0, 1, 2,..., n), 0 ≤ ai ≤ 1, an ≠ 0.
, - , .
1. 543710.
, .
: 8, 82, 83, 84, 85,
(81 = 8, 82 = 64, 83=512, 84 = 4096, 85 = 32768).
, 4096 < 5437 < 32768. 5437 84 . : 5437 = 1 84 + 1341. , :
1341 = 2 83 + 317;
317 = 4 82 + 61;
61 = 7 8 + 5;
.. 5437 = 1 84 + 2 83 + 4 82 + 7 8 + 5;
543710 = 124758
.
5437 8.
5437 8
5 679
5437 = 8 679 + 5. , , , 5 , .. 5. 8.
:
5437 =8 679 + 5
5437 = 8(8 84 + 7) + 5
5437 = 8(8(8 10 + 4) + 7) + 5
5437 = 8(8(8(1 8 + 2) + 4) + 7) + 5 =
= 1 84 + 2 83 + 4 82 + 7 8 + 5.
:
2. 4710. , = 2.
|
|
.
- , - , , .
- , , . :
63758 = 6 83 + 3 82 + 7 8 + 5 = 332510
111012 = 24 + 23 + 22 + 1 = 16 + 8 + 4+1= 2910.