If a and b represent real numbers, then the sum of their squares can be written as the product of complex numbers. This produces the factorization formula: For example, formula_65 can be factored into formula_66.

Kummer also proved Fermat’s last theorem for a considerable class of prime exponents (see regular prime, ideal class group). His methods were closer, perhaps, to p-adic ones than to ideal theory as understood later, though the term ‘ideal’ arose here.

C( i,j ) × C( n,i ) = C( n,i,j ) i = 0 to n, j = 0 to i. [It is important to understand that i, j, n are not exponents here, just sequential labeling indexes.] This table summarizes the properties of the trinomial expansion and the trinomial distribution, and it compares them to the binomial and multinomial expansions and distributions:

Hence these theories can explain feminine and neutral types of defects only. Many congenital heart defects can be diagnosed prenatally by fetal echocardiography. This is a test which can be done during the second trimester of pregnancy, when the woman is about 18–24 weeks pregnant.

Some scholars wish to explain this discrepancy about the 1499 date, considering the version published in 1500 in Toledo to be the first edition; however, there is no positive proof of this, and there are some contradictions:

Petre P. Carp. Petre P. Carp (; also Petrache Carp, Francized Pierre Carp, occasionally Comte Carpe; June 28 or 29, 1837 – June 19, 1919) was a Moldavian, later Romanian statesman, political scientist and culture critic, one of the major representatives of Romanian liberal conservatism, and twice the country’s Prime Minister (1900–1901, 1910–1912).

Bakhtiar was born to Iranian immigrants of Bakhtiari heritage; her father died of oropharyngeal cancer in 2005. Bakhtiar has a younger brother and younger sister. Shapour Bakhtiar is Rudi Bakhtiar’s father’s uncle, the last Prime Minister of Iran under Shah Mohammad Reza Pahlavi, and a great aunt of Bakhtiar’s was the Shah of Iran’s second wife (Soraya Esfandiary).

The photograph was made to mark the end of 165 years of film/chemistry-based photography and the start of the age of digital photography. It was taken using a decommissioned Marine Corps jet hangar (Building #115 at El Toro) transformed into the world’s largest camera to make the world’s largest picture.

It is in great part an ideal picture of that which, in the view of a Brahmin, ought to be law. Donald Davis writes, there is no historical evidence for either an active propagation or implementation of Dharmasastra [Manusmriti] by a ruler or any state – as distinct from other forms of recognizing, respecting and using the text.