Well, Poison Ivy tends to be an extreme environmentalist.

Mseleku was diabetic and at one time had been diagnosed as bipolar.

The polynomial cyclotomic index 4 allows the construction of a new set of algebraic numbers, that of integers of Gauss.

The polynomial cyclotomic index 4 allows the construction of a new set of algebraic numbers, that of integers of Gauss.

He received his doctorate from Columbia University in 1912, after one year of study, for the dissertation The Cyclotomic Quinary Quintic.

In practice, this test is slower than the cyclotomy test for numbers with up to 10,000 digits or so.

He restudied and generalised the mathematical theories of Kummer fields and of cyclotomic fields from the standpoint of abelian varieties over algebraic number fields.

Some 35 years ago, Ken Ribet proved that an abelian variety defined over the maximal cyclotomic extension K of a number field has only finitely many torsion points.

An odd prime number p is defined to be regular if it does not divide the class number of the p-th cyclotomic field Q(ζp), where ζp is a primitive p-th root of unity, it is listed on OEIS: A000927.

An odd prime number p is defined to be regular if it does not divide the class number of the p-th cyclotomic field Q(ζp), where ζp is a p-th root of unity, it is listed on A000927.

Conversely, every abelian extension of the rationals is such a subfield of a cyclotomic field – this is the content of a theorem of Kronecker, usually called the Kronecker–Weber theorem on the grounds that Weber completed the proof.

A deterministic primality test is the cyclotomy test[?]; its runtime can be proven to be O(nclog(log(n))), where n is the number of digits of N and c is a constant independent of n.

A deterministic primality test is the cyclotomy test[?]; its runtime can be proven to be O(nclog(log(n))), where n is the number of digits of N and c is a constant independent of n.