Chemical element named mendelevium in honor of D.I. Mendeleev, the first to arrange the elements in a periodic manner. Most recently, the synthesis of element 118 (since named oganesson) was reported in October 2006, and the synthesis of element 117 (tennessine) was reported in April 2010. Ten materials familiar to various prehistoric cultures are now known to be chemical elements: Carbon, copper, gold, iron, lead, mercury, silver, sulfur, tin, and zinc. Three additional materials now accepted as elements, arsenic, antimony, and bismuth, were recognized as distinct substances prior to 1500 AD. Phosphorus, cobalt, and platinum were isolated before 1750. Most of the
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