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... Equation (17) shows B \ 5C2. Squaring (18) and multiplying both sides by 3 - 5 , we see that B divides each term on the right side so S|34 * 5. For each of the twenty values of B satisfying B\3h • 5 5 we can solve (17) and (18) for A and C9 and verify the only integer solutions (A9 5, C) are (-5, 1, ...
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Algebraic K-theory and sums-of-squares formulas

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The Fundamental Theorem of Algebra

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... expressions and to use the language of algebra with deep comprehension. In the study of operations on polynomials, the special products of standard MA1A2 are first studied as product formulas and related to area models of multiplication. This work lays the foundation for treating these as patterns f ...
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History of algebra

As a branch of mathematics, algebra emerged at the end of 16th century in Europe, with the work of François Viète. Algebra can essentially be considered as doing computations similar to those of arithmetic but with non-numerical mathematical objects. However, until the 19th century, algebra consisted essentially of the theory of equations. For example, the fundamental theorem of algebra belongs to the theory of equations and is not, nowadays, considered as belonging to algebra.This article describes the history of the theory of equations, called here ""algebra"", from the origins to the emergence of algebra as a separate area of mathematics.
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