In this instance it is in fact easy to factor our quartic by treating it as a biquadratic equation; but finding such factorings of a higher degree polynomial can be very difficult.
22.
The leading idea of Baker's work is the solution of biquadratic equations ( and those of a lower degree ) by a geometrical construction, a parabola intersected by a circle.
23.
:: : Apparently quartic functions can be called " biquadratic ", so maybe the fourth power could be a bisquare . talk ) 03 : 03, 21 January 2008 ( UTC)
24.
Several tests and techniques for factoring and solving certain algebraic equations with integer roots for quadratic, cubic, biquadratic, pentic equations, systems of linear equations, and systems of quadratic equations are demonstrated.
25.
The German edition includes all of his papers on number theory : all the proofs of quadratic reciprocity, the determination of the sign of the Gauss sum, the investigations into biquadratic reciprocity, and unpublished notes.
26.
The German edition includes all of Gauss'papers on number theory : all the proofs of quadratic reciprocity, the determination of the sign of the Gauss sum, the investigations into biquadratic reciprocity, and unpublished notes.
27.
He published important contributions to Fermat's last theorem, for which he proved the cases " n " = 5 and " n " = 14, and to the biquadratic reciprocity law.
28.
In the introduction to the fifth and sixth proofs of quadratic reciprocity ( 1818 ) he said that he was publishing these proofs because their techniques ( Gaussian sums, respectively ) can be applied to cubic and biquadratic reciprocity.
29.
Under the supervision of Paul Gordan she wrote her dissertation, " �ber die Bildung des Formensystems der tern�ren biquadratischen Form " ( " On Complete Systems of Invariants for Ternary Biquadratic Forms ", 1907 ).
30.
From his diary and other unpublished sources, it appears that Gauss knew the rules for the cubic and quartic residuacity of integers by 1805, and discovered the full-blown theorems and proofs of cubic and biquadratic reciprocity around 1814.
