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Marie-Sophie Germain (French: [maʁi sɔfi ʒɛʁmɛ̃]; 1 April 1776 – 27 June 1831) was a French mathematician, physicist, and philosopher.Despite initial opposition from her parents and difficulties presented by society, she gained education from books in her father's library, including ones by Euler, and from correspondence with famous mathematicians such as Lagrange, Legendre, and Gauss ...
Sophie Germain's identity. In mathematics, Sophie Germain's identity is a polynomial factorization named after Sophie Germain stating that Beyond its use in elementary algebra, it can also be used in number theory to factorize integers of the special form , and it frequently forms the basis of problems in mathematics competitions. [ 1][ 2][ 3]
Sophie Germain's theorem. In number theory, Sophie Germain's theorem is a statement about the divisibility of solutions to the equation of Fermat's Last Theorem for odd prime .
As a byproduct of this latter work, she proved Sophie Germain's theorem, which verified the first case of Fermat's Last Theorem (namely, the case in which p does not divide xyz) for every odd prime exponent less than 270, [128] [129] and for all primes p such that at least one of 2p + 1, 4p + 1, 8p + 1, 10p + 1, 14p + 1 and 16p + 1 is prime ...
In number theory, a prime number p is a Sophie Germain prime if 2 p + 1 is also prime. The number 2 p + 1 associated with a Sophie Germain prime is called a safe prime. For example, 11 is a Sophie Germain prime and 2 × 11 + 1 = 23 is its associated safe prime. Sophie Germain primes and safe primes have applications in public key cryptography ...
Sophie Germain (1776–1831), French number theorist, physicist, and philosopher, correspondent of Gauss Marie Gernet (1865–1924), first German woman to earn a doctorate in mathematics Nadeschda Gernet (1877–1943), Russian mathematician, student of David Hilbert, worked in the calculus of variations
1827: French mathematician Sophie Germain saw her theorem, known as Sophie Germain's theorem, published in a footnote of a book by the mathematician Adrien-Marie Legendre. [7] [8] In this theorem Germain proved that if x, y, and z are integers and if x 5 + y 5 = z 5 then either x, y, or z must be divisible by 5.
Dirichlet's proof for n = 5 is divided into the two cases (cases I and II) defined by Sophie Germain. In case I, the exponent 5 does not divide the product xyz. In case II, 5 does divide xyz. Case I for n = 5 can be proven immediately by Sophie Germain's theorem(1823) if the auxiliary prime θ = 11.