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The Sophie Germain Identity states that: One can prove this identity simply by multiplying out the right side and verifying that it equals the left. To derive the factoring, we begin by completing the square and then factor as a difference of squares :
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]
Learn about the algebraic identity discovered by Sophie Germain, a French mathematician who worked on Fermat's last theorem and primality testing. See how to use it to factor integers, solve problems, and find applications in number theory.
A Sophie Germain prime is a prime p such that 2p + 1 is also prime. The Germain curvature (also called mean curvature) is (+) /, where k 1 and k 2 are the maximum and minimum values of the normal curvature. Sophie Germain's identity states that for any {x, y},
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Sophie Germain (born April 1, 1776, Paris, France—died June 27, 1831, Paris) was a French mathematician who contributed notably to the study of acoustics, elasticity, and the theory of numbers. As a girl Germain read widely in her father’s library and then later, using the pseudonym of M. Le Blanc, managed to obtain lecture notes for ...
- June Barrow-Green
Oct 28, 1997 · Sophie Germain was a brilliant mathematician who disguised herself as a man to pursue her passion for number theory. She made significant contributions to the study of Fermat's Last Theorem, but faced many challenges and obstacles in a male-dominated field.
Sophie Germain was a 19th-century mathematician who disguised herself as a man to study at the Ecole Polytechnique. She devoted her life to proving Fermat's Last Theorem, a challenge that had eluded generations of mathematicians.
