alumi022.mws

1.找到一個 n 使得 x^n-1 分解後,係數異於 0, -1 and 1 .

> for n from 101 to 105 do factor(x^n-1) od;

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(x-1)*(1+x+x^100+x^99+x^98+x^97+x^96+x^95+x^94+x^93...
(x-1)*(1+x+x^100+x^99+x^98+x^97+x^96+x^95+x^94+x^93...
(x-1)*(1+x+x^100+x^99+x^98+x^97+x^96+x^95+x^94+x^93...
(x-1)*(1+x+x^100+x^99+x^98+x^97+x^96+x^95+x^94+x^93...
(x-1)*(1+x+x^100+x^99+x^98+x^97+x^96+x^95+x^94+x^93...
(x-1)*(1+x+x^100+x^99+x^98+x^97+x^96+x^95+x^94+x^93...

(x-1)*(x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x...
(x-1)*(x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x...
(x-1)*(x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x...
(x-1)*(x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x...
(x-1)*(x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x...
(x-1)*(x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x...

(x-1)*(1+x+x^101+x^100+x^99+x^98+x^97+x^96+x^95+x^9...
(x-1)*(1+x+x^101+x^100+x^99+x^98+x^97+x^96+x^95+x^9...
(x-1)*(1+x+x^101+x^100+x^99+x^98+x^97+x^96+x^95+x^9...
(x-1)*(1+x+x^101+x^100+x^99+x^98+x^97+x^96+x^95+x^9...
(x-1)*(1+x+x^101+x^100+x^99+x^98+x^97+x^96+x^95+x^9...
(x-1)*(1+x+x^101+x^100+x^99+x^98+x^97+x^96+x^95+x^9...

(x-1)*(x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x...
(x-1)*(x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x...
(x-1)*(x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x...
(x-1)*(x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x...

(x-1)*(x^6+x^5+x^4+x^3+x^2+x+1)*(x^4+x^3+x^2+x+1)*(...
(x-1)*(x^6+x^5+x^4+x^3+x^2+x+1)*(x^4+x^3+x^2+x+1)*(...
(x-1)*(x^6+x^5+x^4+x^3+x^2+x+1)*(x^4+x^3+x^2+x+1)*(...
(x-1)*(x^6+x^5+x^4+x^3+x^2+x+1)*(x^4+x^3+x^2+x+1)*(...
(x-1)*(x^6+x^5+x^4+x^3+x^2+x+1)*(x^4+x^3+x^2+x+1)*(...

Ans: n=105

2.因式分解 (((x^2-1.*a)^2-1.*a)^2-1.*a)^2-1.*a-1.*x

> factor((((x^2-a)^2-a)^2-a)^2-a-x);

(-a-x+x^2)*(-a+1+x+x^2)*(1-x^2*a+3*a^4-3*a^3+2*a^2+...
(-a-x+x^2)*(-a+1+x+x^2)*(1-x^2*a+3*a^4-3*a^3+2*a^2+...
(-a-x+x^2)*(-a+1+x+x^2)*(1-x^2*a+3*a^4-3*a^3+2*a^2+...

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