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Quartic reciprocity

Quartic or biquadratic reciprocity is a collection of theorems in elementary and algebraic number theory that state conditions under which the congruence x4 ≡ p (mod q) is solvable; the word "reciprocity" comes from the form of some of these theorems, in that they relate the solvability of the congruence x4 ≡ p (mod q) to that of x4 ≡ q (mod p).

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Integers

Gauss

Gaussian integers

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Quartic reciprocity

Nodes41
Edges40
Triples0
Avg. degree1.95
Density0.04878
Components1

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mod number gauss prime biquadratic reciprocity numbers odd primes integers theory residue first quadratic eisenstein displaystyle form also quartic a2

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