Factoring with cubic integers
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the integer a+bx is smooth,
the algebraic integer a+bz is smooth, where z3=−k. This is the same as asking that its norm, the integer a3 - kb3 shall be smooth (at least, it is when k=2).
We used the method to repeat the factorisation of F7 on an 8-bit computer (2F7=x3+2, where x=243).
KeywordsAlgebraic Integer Factoring Algorithm Rational Integer Algebraic Number Theory Algebraic Number Field
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