1.
定義 Lx(y)=x+1/y,Lx ^2(y)=Lx(Lx(y)),Lx^(n+1) (y)=Lx(Lx^n(y))
n is inter
if Lx^6(x)=p(x)/q(x),而p(x)&q(x)為整數係數多項式
sol 1/Lx^(x)
2.
试为同餘方程組
2x≡1(mod 3)
3x≡1(mod 5)
5x≡1(mod 8)
求最小正整數解
3.
为同餘方程組1050601x≡-1(mod 10610040)
求最小正整數解
數學問題,點名者請回答
2011-02-07 4:02 am
回答 (2)
2011-02-07 4:41 am
✔ 最佳答案
我唔係點名者....但我識答BOR得唔得先
1)Lx(X)=x+(1/x)
Lx^2(X)=Lx(x+1/x)=x+1/x+1/x=x+x/x^2+1=(x^3+2x)/(x^2+1)
.........
Lx^6(x)=x+[(x^5+4x^3+3x)/(x^6+5x^4+6x^2+1)]=[(x^7+6x^5+10x^3+4x)/(x^6+5x^4+6x^2+1)]
so,
1/Lx^6(X)
=[(x^6+5x^4+6x^2+1)/(x^7+6x^5+10x^3+4x)]
2)留意
2x=1(mod3)X40
3x=1(mod5)X24
5x=1(mod8)X15
................
80x=40(mod120).................(1)
72x=24(mod120).................(2)
75x=15(mod120).................(3)
2X[(3)-(2)]-[(1)-(3)]:
2X[3x=-9(mod120)]-[5x=25(mod120)]
[6x=-18(mod120)]-[(5x=25(mod120)]
x=-43(mod120)=77(mod120)
answer:77
3)10610040x=0.................(1)
1050601x=-1......................(2)
(1)-(2)X10:
10610040x=0
10506010x=-10
-----------------------
104030x=10...................(3)
(2)-(3)X10:
1050601x=-1
1040300x=100
-----------------------
10301x=-101.....................(4)
(3)-(4)X10:
104030x=10
103010x=-1010
------------------------
1020x=1020..........................(5)
(4)-(5)X10:
10301x=-101
10200x=10200
--------------------------
101x=-10301.......................(6)
(5)-(6)X10:
1020x=1020
1010x=-103010
-----------------------
10x=104030......................(7)
(6)-(7)X10:
101x=-10301
100x=1040300
----------------------
x=-1050601
so
x=-1050601(mod 10610040)
最少正整數解x=10610040-1050601
=9559439
參考: me
2011-02-07 10:05 pm
so can I answer it?
收錄日期: 2021-04-13 17:48:44
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20110206000051KK00946