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a binomial coefficient. The theorem is named after Ernst Kummer, who proved it in a paper, (Kummer 1852). Kummer's theorem states that for given integers...

z = 1 and then using Gauss's theorem to evaluate the result. A typical example is Kummer's theorem, named for Ernst Kummer: 2 F 1 ( a , b ; 1 + a − b ;...

MR 0465761 Kummer configuration Kummer's congruence Kummer series Kummer theory Kummer's theorem, on prime-power divisors of binomial coefficients Kummer's function...

the Herbrand–Ribet theorem is a result on the class group of certain number fields. It is a strengthening of Ernst Kummer's theorem to the effect that...

In algebraic number theory, the Dedekind–Kummer theorem describes how a prime ideal in a Dedekind domain factors over the domain's integral closure. Let...

multinomial coefficient may be computed using a generalization of Kummer's theorem. By Stirling's approximation, or equivalently the log-gamma function's...

Generalizations of Lucas's theorem for higher prime powers pk are also given by Davis and Webb (1990) and Granville (1997). Kummer's theorem asserts that the largest...

none existed, that valuation would exceed r). This is an instance of Kummer's theorem (since in base p notation the number |G| ends with precisely k + r...

Ankeny–Artin–Chowla. The Bernoulli numbers are related to Fermat's Last Theorem (FLT) by Kummer's theorem, which says: If the odd prime p does not divide any of the...

Ernst Kummer extended this and proved the theorem for all regular primes, leaving irregular primes to be analyzed individually. Building on Kummer's work...

version of Kummer's test was established by Tong. See also for further discussions and new proofs. The provided modification of Kummer's theorem characterizes...

was originally developed by Ernst Eduard Kummer around the 1840s in his pioneering work on Fermat's Last Theorem. The main statements do not depend on the...

\end{aligned}}} Legendre's formula can be used to prove Kummer's theorem. As one special case, it can be used to prove that if n is a positive...

abandoned this experiment, though it remains widely used.[citation needed] Kummer's theorem states that the number of carries involved in adding two numbers in...

Kummer's congruences are some congruences involving Bernoulli numbers, found by Ernst Eduard Kummer (1851). Kubota & Leopoldt (1964) used Kummer's congruences...

formula to the product formula for binomial coefficients produces Kummer's theorem, a similar result on the exponent of each prime in the factorization...

hypergeometric functions: Kummer's (confluent hypergeometric) function M(a, b, z), introduced by Kummer (1837), is a solution to Kummer's differential equation...

Hilbert's Theorem 90 (or Satz 90) is an important result on cyclic extensions of fields (or to one of its generalizations) that leads to Kummer theory....

6, ..., p − 3. Kummer's proof that this is equivalent to the class number definition is strengthened by the Herbrand–Ribet theorem, which states certain...

{R} ^{3}} Hilbert's Theorem 90, an important result on cyclic extensions of fields that leads to Kummer theory Hilbert's basis theorem, in commutative algebra...