A^2+B^2
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A=X^2,B=2*Y^2ãšçœ®ãçŽããš
X^4+4*Y^4
=X^4+4*X^2*Y^2+4*Y^4-4*X^2*Y^2
=(X^2+2*Y^2)^2-(2*X*Y)^2
=(X^2-2*X*Y+2*Y^2)*(X^2+2*X*Y+2*Y^2)
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A^3+B^3=(A+B)*(A^2-A*B+B^2)
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A=X^2,B=3*Y^2ãšçœ®ãçŽããš
X^6+27*Y^6=(X^2+3*Y^2)*(X^4-3*X^2*Y^2+9*Y^4)
=(X^2+3*Y^2)*(X^4+6*X^2*Y^2+9*Y^4-9*X^2*Y^2)
=(X^2+3*Y^2)*((X^2+3*Y^2)^2-(3*X*Y)^2)
=(X^2+3*Y^2)*(x^2-3*X*Y+3*Y^2)*(X^2+3*X*Y+3*Y^2)
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A^5-B^5=(A-B)*(A^4+A^3*B+A^2*B^2+A*B^3+B^4)
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A=5*X^2,B=Y^2ãšçœ®ãçŽããš
(5*X^2-Y^2)*(625*X^8+125*X^6*Y^2+25*X^4*Y^4+5*X^2*Y^6+Y^8)
=(5*X^2-Y^2)*(25*X^4 - 25*X^3*Y + 15*X^2*Y^2 - 5*X*Y^3 + Y^4)*(25*X^4 + 25*X^3*Y + 15*X^2*Y^2 + 5*X*Y^3 + Y^4)
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A^7+B^7=(A+B)*(A^6-A^5*B+A^4*B^2-A^3*B^3+A^2*B^4-A*B^5+B^6)
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A=X^3+1, B=Y^3-1 ãšããã°
A^7+B^7=(X^3+1)^7+(Y^3-1)^7
=(X+Y)(X^2-XY+Y^2)
{(X^18-X^15Y^3+X^12Y^6-X^9Y^9+X^6Y^12-X^3Y^15+Y^18)
+7(X^15-X^12Y^3+X^9Y^6-X^6Y^9+X^3Y^12-Y^15)
+21(X^12-X^9Y^3+X^6Y^6-X^3Y^9+Y^12)+35(X^9-X^6Y^3+X^3Y^6-Y^9)
+35(X^6-X^3Y^3+Y^6)+21(X^3-Y^3)+7}
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(X^18+Y^18) - X^3*Y^3*(X^12+Y^12)+X^6*Y^6*(X^6+Y^6)-X^9*Y^9 +
7*{ (X^15-Y^15) -X^3*Y^3*(X^9-Y^9) +X^6*Y^6*(X^3-Y^3)} +
21*{(X^12+Y^12) -X^3*Y^3*(X^6+Y^6) +(X^3-Y^3)+X^6*Y^6} +
35*{ (X^9-Y^9) -X^3*Y^3*(X^3-Y^3) +(X^6+Y^6)-X^3*Y^3} +
7
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A=7*X^2,B=Y^2ãšçœ®ããŠåºæ¥ã
823543*X^14+Y^14=(7*X^2+Y^2)*(117649*X^12 - 16807*Y^2*X^10 + 2401*Y^4*X^8 - 343*Y^6*X^6 + 49*Y^8*X^4 - 7*Y^10*X^2 + Y^12)
=(7*X^2+Y^2)
* (343*X^6 - 343*Y*X^5 + 147*Y^2*X^4 - 49*Y^3*X^3 + 21*Y^4*X^2 - 7*Y^5*X + Y^6)
ããããããããã* (343*X^6 + 343*Y*X^5 + 147*Y^2*X^4 + 49*Y^3*X^3 + 21*Y^4*X^2 + 7*Y^5*X + Y^6)
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