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- - **Casus of x^3+1**
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Casus of x^3+1Do You know that
[TEX](2*(x^2+1)^3-7))^2\equiv3^4\ mod\ x^3+1[/TEX] for all x in Z, abs(x)>=5??? |

[QUOTE=RomanM;595306]Do You know that
[TEX](2*(x^2+1)^3-7))^2\equiv3^4\ mod\ x^3+1[/TEX] for all x in Z, abs(x)>=5???[/QUOTE]If you want to check this as a polynomial congruence, you might first try finding 2*(x^2+1)^3 - 7 (mod x^3 + 1) by polynomial division with quotient and remainder 2*(x^2+1)^3 - 7 = (x^3 + 1)*q(x) + r(x); q(x), r(x) polynomials The remainder r(x) will be a polynomial of degree less than 3. [b]EDIT:[/b] There are even slicker and quicker ways, but I'm not telling. |

[QUOTE=RomanM;595306]Do You know that
[TEX](2*(x^2+1)^3-7))^2\equiv3^4\ mod\ x^3+1[/TEX] for all x in Z, abs(x)>=5???[/QUOTE] Yes, we know. :smile: |

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