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In mathematics, Eisenstein's theorem, named after the German mathematician Gotthold Eisenstein, applies to the coefficients of any power series which is...

In mathematics, Eisenstein's criterion gives a sufficient condition for a polynomial with integer coefficients to be irreducible over the rational numbers...

review Eisenstein's criterion Eisenstein ideal Eisenstein integer Eisenstein prime Eisenstein reciprocity Eisenstein sum Eisenstein series Eisenstein's theorem...

posthumous papers, but it is not clear if they are his or Eisenstein's. Jacobi published several theorems about cubic residuacity in 1827, but no proofs. In...

In algebra, the rational root theorem (or rational root test, rational zero theorem, rational zero test or p/q theorem) states a constraint on rational...

In complex analysis, the residue theorem, sometimes called Cauchy's residue theorem, is a powerful tool to evaluate line integrals of analytic functions...

In number theory, the law of quadratic reciprocity is a theorem about modular arithmetic that gives conditions for the solvability of quadratic equations...

reciprocity laws, including a proof of Eisenstein's law using Gauss and Jacobi sums that is based on Eisenstein's original proof. In 1922 Takagi proved...

mathematics, the fundamental theorem of arithmetic, also called the unique factorization theorem and prime factorization theorem, states that every integer...

conjugate root theorem Algebraic element Horner scheme Rational root theorem Gauss's lemma (polynomial) Irreducible polynomial Eisenstein's criterion Primitive...

In number theory, Jacobi's four-square theorem gives a formula for the number of ways that a given positive integer n can be represented as the sum of...

algebraic function solutions. The initial result of this type was Eisenstein's theorem. Hasse principle The Hasse principle states that solubility for a...

triangle formed by three of the points has large area. Another example is Eisenstein's criterion, a test for whether a polynomial is irreducible based on divisibility...

In number theory, Bertrand's postulate is the theorem that for any integer n > 3 {\displaystyle n>3} , there exists at least one prime number p {\displaystyle...

hypothesis is true, then the theorem is true. If the generalized Riemann hypothesis is false, then the theorem is true. Thus, the theorem is true!! Care should...

established by Emil Artin in a series of papers (1924; 1927; 1930), is a general theorem in number theory that forms a central part of global class field theory...

because of their close connection to perfect numbers: the Euclid–Euler theorem asserts a one-to-one correspondence between even perfect numbers and Mersenne...

superior. This result is Grönwall's theorem, published in 1913 (Grönwall 1913). His proof uses Mertens' third theorem, which says that: lim n → ∞ 1 log...

Greek mathematicians in the case of integers. They proved the fundamental theorem of arithmetic, which asserts that every positive integer may be factored...

scholar. He gave the second and third complete proofs of the fundamental theorem of algebra, made contributions to number theory, and developed the theories...