Definition of Biquadratic root of a number. Meaning of Biquadratic root of a number. Synonyms of Biquadratic root of a number

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Definition of Biquadratic root of a number

Biquadratic root of a number
Biquadratic Bi`quad*rat"ic, a. [Pref. bi- + quadratic: cf. F. biquadratique.] (Math.) Of or pertaining to the biquadrate, or fourth power. Biquadratic equation (Alg.), an equation of the fourth degree, or an equation in some term of which the unknown quantity is raised to the fourth power. Biquadratic root of a number, the square root of the square root of that number. Thus the square root of 81 is 9, and the square root of 9 is 3, which is the biquadratic root of 81. Hutton.

Meaning of Biquadratic root of a number from wikipedia

- arithmetic, a number g is a primitive root modulo n if every number a coprime to n is congruent to a power of g modulo n. That is, g is a primitive root modulo n...
- [Of course just as the higher arithmetic has been investigated so far in problems only among real integer numbers, so theorems regarding biquadratic residues...
- objects of study. Algebraic number field Gaussian integer, Gaussian rational Quadratic field Cyclotomic field Cubic field Biquadratic field Quadratic reciprocity...
- Sometimes the term biquadratic is used instead of quartic, but, usually, biquadratic function refers to a quadratic function of a square (or, equivalently...
- 4 = 0 {\displaystyle a(x-l)^{4}=0} , for some real number l {\displaystyle l} . This case can always be reduced to a biquadratic equation. Multiplicity-3...
- may be reduced to a quadratic equation by a change of variable provided it is either biquadratic (b = d = 0) or quasi-palindromic (e = a, d = b). Some cubic...
- biquadratic reciprocity have consecutively numbered sections: the first contains §§ 1–23 and the second §§ 24–76. Footnotes referencing these are of the...
- Generalizations of Gauss's lemma can be used to compute higher power residue symbols. In his second monograph on biquadratic reciprocity,: §§69–71  Gauss used a fourth-power...
- Quartic or biquadratic reciprocity is a collection of theorems in elementary and algebraic number theory that state conditions under which the congruence...
- into biquadratic reciprocity, and unpublished notes. Gauss, Carl Friedrich (1986), Disquisitiones Arithemeticae, translated by Clarke, Arthur A. (Second...