Period 6 element heavy metal, lead is a neurotoxin that accumulates both in soft tissues and the bones. Lead poisoning has been documented from ancient Rome, ancient Greece, and ancient China. Bismuth is a chemical element with symbol Bi and atomic number 83. Bismuth, a trivalent other metal, chemically resembles arsenic and antimony. Elemental bismuth may occur naturally uncombined, although its sulfide and oxide form important commercial ores. The free element is 86% as dense as lead. It is a brittle metal with a silvery white color when newly made, but often seen in air with a pink tinge owing to the surface
Hilbert symbol reciprocity law follows from the Artin reciprocity law and the definition of the Hilbert symbol in terms of the Artin symbol. If "K" is a number field containing the "n"th roots of unity, "p" is a prime ideal not dividing "n", π is a prime element of the local field of "p", and "a" is coprime to "p", then the power residue symbol () is related to the Hilbert symbol by The power residue symbol is extended to fractional ideals by multiplicativity, and defined for elements of the number field by putting ()=() where ("b") is the principal ideal generated