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Gauss published the first and second proofs of the law of quadratic reciprocity on arts 125–146 and 262 of Disquisitiones Arithmeticae in 1801.. In number theory, the law of quadratic reciprocity is a theorem about modular arithmetic that gives conditions for the solvability of quadratic equations modulo prime numbers.
The use of LaTeX in a piped link or in a section heading does not appear in blue in the linked text or the table of content. Moreover, links to section headings containing LaTeX formulas do not always work as expected. Finally, having many LaTeX formulas may significantly increase the processing time of a page.
This is a list of notable theorems. Lists of theorems and similar statements include: List of algebras; List of algorithms; List of axioms; List of conjectures; List of data structures; List of derivatives and integrals in alternative calculi; List of equations; List of fundamental theorems; List of hypotheses; List of inequalities; Lists of ...
In Euclid's Elements the theorem is stated in Book IX, Proposition 20: [9] Prime numbers are more than any assigned multitude of prime numbers. Depending on how we formally write the above statement, the usual proof takes either the form of a proof by contradiction or a refutation by contradiction.
It is inspired by the typographic practice of end marks, an element that marks the end of an article. [1] [2] In Unicode, it is represented as character U+220E ∎ END OF PROOF. Its graphic form varies, as it may be a hollow or filled rectangle or square. In AMS-LaTeX, the symbol is automatically appended at the end of a proof environment ...
Rank–nullity theorem. The rank–nullity theorem is a theorem in linear algebra, which asserts: the number of columns of a matrix M is the sum of the rank of M and the nullity of M; and; the dimension of the domain of a linear transformation f is the sum of the rank of f (the dimension of the image of f) and the nullity of f (the dimension of ...
The order of operations, that is, the order in which the operations in an expression are usually performed, results from a convention adopted throughout mathematics, science, technology and many computer programming languages.
Consistent with its use for derivability, a "⊢" followed by an expression without anything preceding it denotes a theorem, which is to say that the expression can be derived from the rules using an empty set of axioms. As such, the expression means that Q is a theorem in the system.