- 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...
-
Quartic or
biquadratic reciprocity is
a collection of theorems in
elementary and
algebraic number theory that
state conditions under which the congruence...
-
Sometimes the term
biquadratic is used
instead of quartic, but, usually,
biquadratic function refers to
a quadratic function of a square (or, equivalently...
-
biquadratic reciprocity have
consecutively numbered sections: the
first contains §§ 1–23 and the
second §§ 24–76.
Footnotes referencing these are
of the...
- a(x−l)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...
- 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 and quartic...
-
objects of study.
Algebraic number field Gaussian integer,
Gaussian rational Quadratic field Cyclotomic field Cubic field Biquadratic field Quadratic reciprocity...
-
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...
-
determination of the sign of the
Gauss sum, the
investigations into
biquadratic reciprocity, and
unpublished notes. Gauss, Carl
Friedrich (1986), Disquisitiones...
- 2001). "Computing
Minimal Equal Sums
Of Like Powers: Best
Known Solutions".
Retrieved 17 July 2017. Weisstein, Eric W. "
Biquadratic Number". MathWorld....