원분다항식(cyclotomic polynomial)

이 항목의 스프링노트 원문주소

• 원분다항식(cyclotomic polynomial)

 

 

정의

\(\Phi_n(X) = \prod_\omega (X-\omega)\)

\(\omega\) : primitive n-th 단위근(root of unity)

 

예

\(\Phi_1(X) = X-1\)

\(\Phi_2(X) = X+1\)

\(\Phi_3(X) = X^2 + X + 1\)

\(\Phi_6(X) = X^2 - X + 1\)

\(\Phi_9(X) = X^6 + X^3 + 1\)

\(\Phi_{15}(X) = X^8 - X^7 + X^5 - X^4 + X^3 - X + 1\)

 

 

Subscript[\[CapitalPhi], 1](x)=x-1
Subscript[\[CapitalPhi], 2](x)=x+1
Subscript[\[CapitalPhi], 3](x)=x^2+x+1
Subscript[\[CapitalPhi], 4](x)=x^2+1
Subscript[\[CapitalPhi], 5](x)=x^4+x^3+x^2+x+1
Subscript[\[CapitalPhi], 6](x)=x^2-x+1
Subscript[\[CapitalPhi], 7](x)=x^6+x^5+x^4+x^3+x^2+x+1
Subscript[\[CapitalPhi], 8](x)=x^4+1
Subscript[\[CapitalPhi], 9](x)=x^6+x^3+1
Subscript[\[CapitalPhi], 10](x)=x^4-x^3+x^2-x+1
Subscript[\[CapitalPhi], 11](x)=x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1
Subscript[\[CapitalPhi], 12](x)=x^4-x^2+1
Subscript[\[CapitalPhi], 13](x)=x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1
Subscript[\[CapitalPhi], 14](x)=x^6-x^5+x^4-x^3+x^2-x+1
Subscript[\[CapitalPhi], 15](x)=x^8-x^7+x^5-x^4+x^3-x+1
Subscript[\[CapitalPhi], 16](x)=x^8+1
Subscript[\[CapitalPhi], 17](x)=x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1
Subscript[\[CapitalPhi], 18](x)=x^6-x^3+1
Subscript[\[CapitalPhi], 19](x)=x^18+x^17+x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1
Subscript[\[CapitalPhi], 20](x)=x^8-x^6+x^4-x^2+1
Subscript[\[CapitalPhi], 21](x)=x^12-x^11+x^9-x^8+x^6-x^4+x^3-x+1
Subscript[\[CapitalPhi], 22](x)=x^10-x^9+x^8-x^7+x^6-x^5+x^4-x^3+x^2-x+1
Subscript[\[CapitalPhi], 23](x)=x^22+x^21+x^20+x^19+x^18+x^17+x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1
Subscript[\[CapitalPhi], 24](x)=x^8-x^4+1
Subscript[\[CapitalPhi], 25](x)=x^20+x^15+x^10+x^5+1
Subscript[\[CapitalPhi], 26](x)=x^12-x^11+x^10-x^9+x^8-x^7+x^6-x^5+x^4-x^3+x^2-x+1
Subscript[\[CapitalPhi], 27](x)=x^18+x^9+1
Subscript[\[CapitalPhi], 28](x)=x^12-x^10+x^8-x^6+x^4-x^2+1
Subscript[\[CapitalPhi], 29](x)=x^28+x^27+x^26+x^25+x^24+x^23+x^22+x^21+x^20+x^19+x^18+x^17+x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1
Subscript[\[CapitalPhi], 30](x)=x^8+x^7-x^5-x^4-x^3+x+1
Subscript[\[CapitalPhi], 31](x)=x^30+x^29+x^28+x^27+x^26+x^25+x^24+x^23+x^22+x^21+x^20+x^19+x^18+x^17+x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1
Subscript[\[CapitalPhi], 32](x)=x^16+1
Subscript[\[CapitalPhi], 33](x)=x^20-x^19+x^17-x^16+x^14-x^13+x^11-x^10+x^9-x^7+x^6-x^4+x^3-x+1
Subscript[\[CapitalPhi], 34](x)=x^16-x^15+x^14-x^13+x^12-x^11+x^10-x^9+x^8-x^7+x^6-x^5+x^4-x^3+x^2-x+1
Subscript[\[CapitalPhi], 35](x)=x^24-x^23+x^19-x^18+x^17-x^16+x^14-x^13+x^12-x^11+x^10-x^8+x^7-x^6+x^5-x+1
Subscript[\[CapitalPhi], 36](x)=x^12-x^6+1
Subscript[\[CapitalPhi], 37](x)=x^36+x^35+x^34+x^33+x^32+x^31+x^30+x^29+x^28+x^27+x^26+x^25+x^24+x^23+x^22+x^21+x^20+x^19+x^18+x^17+x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1
Subscript[\[CapitalPhi], 38](x)=x^18-x^17+x^16-x^15+x^14-x^13+x^12-x^11+x^10-x^9+x^8-x^7+x^6-x^5+x^4-x^3+x^2-x+1
Subscript[\[CapitalPhi], 39](x)=x^24-x^23+x^21-x^20+x^18-x^17+x^15-x^14+x^12-x^10+x^9-x^7+x^6-x^4+x^3-x+1
Subscript[\[CapitalPhi], 40](x)=x^16-x^12+x^8-x^4+1
Subscript[\[CapitalPhi], 41](x)=x^40+x^39+x^38+x^37+x^36+x^35+x^34+x^33+x^32+x^31+x^30+x^29+x^28+x^27+x^26+x^25+x^24+x^23+x^22+x^21+x^20+x^19+x^18+x^17+x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1
Subscript[\[CapitalPhi], 42](x)=x^12+x^11-x^9-x^8+x^6-x^4-x^3+x+1
Subscript[\[CapitalPhi], 43](x)=x^42+x^41+x^40+x^39+x^38+x^37+x^36+x^35+x^34+x^33+x^32+x^31+x^30+x^29+x^28+x^27+x^26+x^25+x^24+x^23+x^22+x^21+x^20+x^19+x^18+x^17+x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1
Subscript[\[CapitalPhi], 44](x)=x^20-x^18+x^16-x^14+x^12-x^10+x^8-x^6+x^4-x^2+1
Subscript[\[CapitalPhi], 45](x)=x^24-x^21+x^15-x^12+x^9-x^3+1
Subscript[\[CapitalPhi], 46](x)=x^22-x^21+x^20-x^19+x^18-x^17+x^16-x^15+x^14-x^13+x^12-x^11+x^10-x^9+x^8-x^7+x^6-x^5+x^4-x^3+x^2-x+1
Subscript[\[CapitalPhi], 47](x)=x^46+x^45+x^44+x^43+x^42+x^41+x^40+x^39+x^38+x^37+x^36+x^35+x^34+x^33+x^32+x^31+x^30+x^29+x^28+x^27+x^26+x^25+x^24+x^23+x^22+x^21+x^20+x^19+x^18+x^17+x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1
Subscript[\[CapitalPhi], 48](x)=x^16-x^8+1
Subscript[\[CapitalPhi], 49](x)=x^42+x^35+x^28+x^21+x^14+x^7+1
Subscript[\[CapitalPhi], 50](x)=x^20-x^15+x^10-x^5+1
Subscript[\[CapitalPhi], 51](x)=x^32-x^31+x^29-x^28+x^26-x^25+x^23-x^22+x^20-x^19+x^17-x^16+x^15-x^13+x^12-x^10+x^9-x^7+x^6-x^4+x^3-x+1
Subscript[\[CapitalPhi], 52](x)=x^24-x^22+x^20-x^18+x^16-x^14+x^12-x^10+x^8-x^6+x^4-x^2+1
Subscript[\[CapitalPhi], 53](x)=x^52+x^51+x^50+x^49+x^48+x^47+x^46+x^45+x^44+x^43+x^42+x^41+x^40+x^39+x^38+x^37+x^36+x^35+x^34+x^33+x^32+x^31+x^30+x^29+x^28+x^27+x^26+x^25+x^24+x^23+x^22+x^21+x^20+x^19+x^18+x^17+x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1
Subscript[\[CapitalPhi], 54](x)=x^18-x^9+1
Subscript[\[CapitalPhi], 55](x)=x^40-x^39+x^35-x^34+x^30-x^28+x^25-x^23+x^20-x^17+x^15-x^12+x^10-x^6+x^5-x+1
Subscript[\[CapitalPhi], 56](x)=x^24-x^20+x^16-x^12+x^8-x^4+1
Subscript[\[CapitalPhi], 57](x)=x^36-x^35+x^33-x^32+x^30-x^29+x^27-x^26+x^24-x^23+x^21-x^20+x^18-x^16+x^15-x^13+x^12-x^10+x^9-x^7+x^6-x^4+x^3-x+1
Subscript[\[CapitalPhi], 58](x)=x^28-x^27+x^26-x^25+x^24-x^23+x^22-x^21+x^20-x^19+x^18-x^17+x^16-x^15+x^14-x^13+x^12-x^11+x^10-x^9+x^8-x^7+x^6-x^5+x^4-x^3+x^2-x+1
Subscript[\[CapitalPhi], 59](x)=x^58+x^57+x^56+x^55+x^54+x^53+x^52+x^51+x^50+x^49+x^48+x^47+x^46+x^45+x^44+x^43+x^42+x^41+x^40+x^39+x^38+x^37+x^36+x^35+x^34+x^33+x^32+x^31+x^30+x^29+x^28+x^27+x^26+x^25+x^24+x^23+x^22+x^21+x^20+x^19+x^18+x^17+x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1
Subscript[\[CapitalPhi], 60](x)=x^16+x^14-x^10-x^8-x^6+x^2+1
Subscript[\[CapitalPhi], 61](x)=x^60+x^59+x^58+x^57+x^56+x^55+x^54+x^53+x^52+x^51+x^50+x^49+x^48+x^47+x^46+x^45+x^44+x^43+x^42+x^41+x^40+x^39+x^38+x^37+x^36+x^35+x^34+x^33+x^32+x^31+x^30+x^29+x^28+x^27+x^26+x^25+x^24+x^23+x^22+x^21+x^20+x^19+x^18+x^17+x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1
Subscript[\[CapitalPhi], 62](x)=x^30-x^29+x^28-x^27+x^26-x^25+x^24-x^23+x^22-x^21+x^20-x^19+x^18-x^17+x^16-x^15+x^14-x^13+x^12-x^11+x^10-x^9+x^8-x^7+x^6-x^5+x^4-x^3+x^2-x+1
Subscript[\[CapitalPhi], 63](x)=x^36-x^33+x^27-x^24+x^18-x^12+x^9-x^3+1
Subscript[\[CapitalPhi], 64](x)=x^32+1
Subscript[\[CapitalPhi], 65](x)=x^48-x^47+x^43-x^42+x^38-x^37+x^35-x^34+x^33-x^32+x^30-x^29+x^28-x^27+x^25-x^24+x^23-x^21+x^20-x^19+x^18-x^16+x^15-x^14+x^13-x^11+x^10-x^6+x^5-x+1
Subscript[\[CapitalPhi], 66](x)=x^20+x^19-x^17-x^16+x^14+x^13-x^11-x^10-x^9+x^7+x^6-x^4-x^3+x+1
Subscript[\[CapitalPhi], 67](x)=x^66+x^65+x^64+x^63+x^62+x^61+x^60+x^59+x^58+x^57+x^56+x^55+x^54+x^53+x^52+x^51+x^50+x^49+x^48+x^47+x^46+x^45+x^44+x^43+x^42+x^41+x^40+x^39+x^38+x^37+x^36+x^35+x^34+x^33+x^32+x^31+x^30+x^29+x^28+x^27+x^26+x^25+x^24+x^23+x^22+x^21+x^20+x^19+x^18+x^17+x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1
Subscript[\[CapitalPhi], 68](x)=x^32-x^30+x^28-x^26+x^24-x^22+x^20-x^18+x^16-x^14+x^12-x^10+x^8-x^6+x^4-x^2+1
Subscript[\[CapitalPhi], 69](x)=x^44-x^43+x^41-x^40+x^38-x^37+x^35-x^34+x^32-x^31+x^29-x^28+x^26-x^25+x^23-x^22+x^21-x^19+x^18-x^16+x^15-x^13+x^12-x^10+x^9-x^7+x^6-x^4+x^3-x+1
Subscript[\[CapitalPhi], 70](x)=x^24+x^23-x^19-x^18-x^17-x^16+x^14+x^13+x^12+x^11+x^10-x^8-x^7-x^6-x^5+x+1
Subscript[\[CapitalPhi], 71](x)=x^70+x^69+x^68+x^67+x^66+x^65+x^64+x^63+x^62+x^61+x^60+x^59+x^58+x^57+x^56+x^55+x^54+x^53+x^52+x^51+x^50+x^49+x^48+x^47+x^46+x^45+x^44+x^43+x^42+x^41+x^40+x^39+x^38+x^37+x^36+x^35+x^34+x^33+x^32+x^31+x^30+x^29+x^28+x^27+x^26+x^25+x^24+x^23+x^22+x^21+x^20+x^19+x^18+x^17+x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1
Subscript[\[CapitalPhi], 72](x)=x^24-x^12+1
Subscript[\[CapitalPhi], 73](x)=x^72+x^71+x^70+x^69+x^68+x^67+x^66+x^65+x^64+x^63+x^62+x^61+x^60+x^59+x^58+x^57+x^56+x^55+x^54+x^53+x^52+x^51+x^50+x^49+x^48+x^47+x^46+x^45+x^44+x^43+x^42+x^41+x^40+x^39+x^38+x^37+x^36+x^35+x^34+x^33+x^32+x^31+x^30+x^29+x^28+x^27+x^26+x^25+x^24+x^23+x^22+x^21+x^20+x^19+x^18+x^17+x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1
Subscript[\[CapitalPhi], 74](x)=x^36-x^35+x^34-x^33+x^32-x^31+x^30-x^29+x^28-x^27+x^26-x^25+x^24-x^23+x^22-x^21+x^20-x^19+x^18-x^17+x^16-x^15+x^14-x^13+x^12-x^11+x^10-x^9+x^8-x^7+x^6-x^5+x^4-x^3+x^2-x+1
Subscript[\[CapitalPhi], 75](x)=x^40-x^35+x^25-x^20+x^15-x^5+1
Subscript[\[CapitalPhi], 76](x)=x^36-x^34+x^32-x^30+x^28-x^26+x^24-x^22+x^20-x^18+x^16-x^14+x^12-x^10+x^8-x^6+x^4-x^2+1
Subscript[\[CapitalPhi], 77](x)=x^60-x^59+x^53-x^52+x^49-x^48+x^46-x^45+x^42-x^41+x^39-x^37+x^35-x^34+x^32-x^30+x^28-x^26+x^25-x^23+x^21-x^19+x^18-x^15+x^14-x^12+x^11-x^8+x^7-x+1
Subscript[\[CapitalPhi], 78](x)=x^24+x^23-x^21-x^20+x^18+x^17-x^15-x^14+x^12-x^10-x^9+x^7+x^6-x^4-x^3+x+1
Subscript[\[CapitalPhi], 79](x)=x^78+x^77+x^76+x^75+x^74+x^73+x^72+x^71+x^70+x^69+x^68+x^67+x^66+x^65+x^64+x^63+x^62+x^61+x^60+x^59+x^58+x^57+x^56+x^55+x^54+x^53+x^52+x^51+x^50+x^49+x^48+x^47+x^46+x^45+x^44+x^43+x^42+x^41+x^40+x^39+x^38+x^37+x^36+x^35+x^34+x^33+x^32+x^31+x^30+x^29+x^28+x^27+x^26+x^25+x^24+x^23+x^22+x^21+x^20+x^19+x^18+x^17+x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1
Subscript[\[CapitalPhi], 80](x)=x^32-x^24+x^16-x^8+1
Subscript[\[CapitalPhi], 81](x)=x^54+x^27+1
Subscript[\[CapitalPhi], 82](x)=x^40-x^39+x^38-x^37+x^36-x^35+x^34-x^33+x^32-x^31+x^30-x^29+x^28-x^27+x^26-x^25+x^24-x^23+x^22-x^21+x^20-x^19+x^18-x^17+x^16-x^15+x^14-x^13+x^12-x^11+x^10-x^9+x^8-x^7+x^6-x^5+x^4-x^3+x^2-x+1
Subscript[\[CapitalPhi], 83](x)=x^82+x^81+x^80+x^79+x^78+x^77+x^76+x^75+x^74+x^73+x^72+x^71+x^70+x^69+x^68+x^67+x^66+x^65+x^64+x^63+x^62+x^61+x^60+x^59+x^58+x^57+x^56+x^55+x^54+x^53+x^52+x^51+x^50+x^49+x^48+x^47+x^46+x^45+x^44+x^43+x^42+x^41+x^40+x^39+x^38+x^37+x^36+x^35+x^34+x^33+x^32+x^31+x^30+x^29+x^28+x^27+x^26+x^25+x^24+x^23+x^22+x^21+x^20+x^19+x^18+x^17+x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1
Subscript[\[CapitalPhi], 84](x)=x^24+x^22-x^18-x^16+x^12-x^8-x^6+x^2+1
Subscript[\[CapitalPhi], 85](x)=x^64-x^63+x^59-x^58+x^54-x^53+x^49-x^48+x^47-x^46+x^44-x^43+x^42-x^41+x^39-x^38+x^37-x^36+x^34-x^33+x^32-x^31+x^30-x^28+x^27-x^26+x^25-x^23+x^22-x^21+x^20-x^18+x^17-x^16+x^15-x^11+x^10-x^6+x^5-x+1
Subscript[\[CapitalPhi], 86](x)=x^42-x^41+x^40-x^39+x^38-x^37+x^36-x^35+x^34-x^33+x^32-x^31+x^30-x^29+x^28-x^27+x^26-x^25+x^24-x^23+x^22-x^21+x^20-x^19+x^18-x^17+x^16-x^15+x^14-x^13+x^12-x^11+x^10-x^9+x^8-x^7+x^6-x^5+x^4-x^3+x^2-x+1
Subscript[\[CapitalPhi], 87](x)=x^56-x^55+x^53-x^52+x^50-x^49+x^47-x^46+x^44-x^43+x^41-x^40+x^38-x^37+x^35-x^34+x^32-x^31+x^29-x^28+x^27-x^25+x^24-x^22+x^21-x^19+x^18-x^16+x^15-x^13+x^12-x^10+x^9-x^7+x^6-x^4+x^3-x+1
Subscript[\[CapitalPhi], 88](x)=x^40-x^36+x^32-x^28+x^24-x^20+x^16-x^12+x^8-x^4+1
Subscript[\[CapitalPhi], 89](x)=x^88+x^87+x^86+x^85+x^84+x^83+x^82+x^81+x^80+x^79+x^78+x^77+x^76+x^75+x^74+x^73+x^72+x^71+x^70+x^69+x^68+x^67+x^66+x^65+x^64+x^63+x^62+x^61+x^60+x^59+x^58+x^57+x^56+x^55+x^54+x^53+x^52+x^51+x^50+x^49+x^48+x^47+x^46+x^45+x^44+x^43+x^42+x^41+x^40+x^39+x^38+x^37+x^36+x^35+x^34+x^33+x^32+x^31+x^30+x^29+x^28+x^27+x^26+x^25+x^24+x^23+x^22+x^21+x^20+x^19+x^18+x^17+x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1
Subscript[\[CapitalPhi], 90](x)=x^24+x^21-x^15-x^12-x^9+x^3+1
Subscript[\[CapitalPhi], 91](x)=x^72-x^71+x^65-x^64+x^59-x^57+x^52-x^50+x^46-x^43+x^39-x^36+x^33-x^29+x^26-x^22+x^20-x^15+x^13-x^8+x^7-x+1
Subscript[\[CapitalPhi], 92](x)=x^44-x^42+x^40-x^38+x^36-x^34+x^32-x^30+x^28-x^26+x^24-x^22+x^20-x^18+x^16-x^14+x^12-x^10+x^8-x^6+x^4-x^2+1
Subscript[\[CapitalPhi], 93](x)=x^60-x^59+x^57-x^56+x^54-x^53+x^51-x^50+x^48-x^47+x^45-x^44+x^42-x^41+x^39-x^38+x^36-x^35+x^33-x^32+x^30-x^28+x^27-x^25+x^24-x^22+x^21-x^19+x^18-x^16+x^15-x^13+x^12-x^10+x^9-x^7+x^6-x^4+x^3-x+1
Subscript[\[CapitalPhi], 94](x)=x^46-x^45+x^44-x^43+x^42-x^41+x^40-x^39+x^38-x^37+x^36-x^35+x^34-x^33+x^32-x^31+x^30-x^29+x^28-x^27+x^26-x^25+x^24-x^23+x^22-x^21+x^20-x^19+x^18-x^17+x^16-x^15+x^14-x^13+x^12-x^11+x^10-x^9+x^8-x^7+x^6-x^5+x^4-x^3+x^2-x+1
Subscript[\[CapitalPhi], 95](x)=x^72-x^71+x^67-x^66+x^62-x^61+x^57-x^56+x^53-x^51+x^48-x^46+x^43-x^41+x^38-x^36+x^34-x^31+x^29-x^26+x^24-x^21+x^19-x^16+x^15-x^11+x^10-x^6+x^5-x+1
Subscript[\[CapitalPhi], 96](x)=x^32-x^16+1
Subscript[\[CapitalPhi], 97](x)=x^96+x^95+x^94+x^93+x^92+x^91+x^90+x^89+x^88+x^87+x^86+x^85+x^84+x^83+x^82+x^81+x^80+x^79+x^78+x^77+x^76+x^75+x^74+x^73+x^72+x^71+x^70+x^69+x^68+x^67+x^66+x^65+x^64+x^63+x^62+x^61+x^60+x^59+x^58+x^57+x^56+x^55+x^54+x^53+x^52+x^51+x^50+x^49+x^48+x^47+x^46+x^45+x^44+x^43+x^42+x^41+x^40+x^39+x^38+x^37+x^36+x^35+x^34+x^33+x^32+x^31+x^30+x^29+x^28+x^27+x^26+x^25+x^24+x^23+x^22+x^21+x^20+x^19+x^18+x^17+x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1
Subscript[\[CapitalPhi], 98](x)=x^42-x^35+x^28-x^21+x^14-x^7+1
Subscript[\[CapitalPhi], 99](x)=x^60-x^57+x^51-x^48+x^42-x^39+x^33-x^30+x^27-x^21+x^18-x^12+x^9-x^3+1
Subscript[\[CapitalPhi], 100](x)=x^40-x^30+x^20-x^10+1

 

역사

• 수학사연표

 

 

 

 

 

 

관련된 다른 주제들

•  오일러의 totient 함수
• 가우스와 정17각형의 작도

 

 

관련도서 및 추천도서

• 도서내검색
  
  • http://books.google.com/books?q=
  • http://book.daum.net/search/contentSearch.do?query=
• 도서검색
  
  • http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
  • http://book.daum.net/search/mainSearch.do?query=

 

 

사전형태의 참고자료

• http://ko.wikipedia.org/wiki/
• http://en.wikipedia.org/wiki/Cyclotomic_polynomial
• http://en.wikipedia.org/wiki/
• http://www88.wolframalpha.com/input/?i=cyclotomic+polynomial
• 대한수학회 수학 학술 용어집
  
  • http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=eng_term&fstr=cyclotomic
• 
  

 

관련기사

• 네이버 뉴스 검색 (키워드 수정)
  
  • http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=
  • http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=
  • http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=
  • http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=
  • http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=

 

 

블로그

• 구글 블로그 검색 http://blogsearch.google.com/blogsearch?q=
• 트렌비 블로그 검색 http://www.trenb.com/search.qst?q=