In mathematics, the **Kummer–Vandiver conjecture**, or **Vandiver conjecture**, states that a prime *p* does not divide the class number *h _{K}* of the maximal real subfield of the

*p*-th cyclotomic field. The conjecture was first made by Ernst Kummer in 1849 December 28 and 1853 April 24 in letters to Leopold Kronecker, reprinted in (Kummer 1975, pages 84, 93, 123–124), and independently rediscovered around 1920 by Philipp Furtwängler and Harry Vandiver (1946, p. 576),

As of 2011, there is no particularly strong evidence either for or against the conjecture and it is unclear whether it is true or false, though it is likely that counterexamples are very rare.

Read more about Kummer–Vandiver Conjecture: Background, Evidence For and Against The Kummer–Vandiver Conjecture, Consequences of The Kummer–Vandiver Conjecture

### Other articles related to "conjecture":

**Kummer–Vandiver Conjecture**

... Kurihara (1992) showed that the

**conjecture**is equivalent to a statement in the algebraic K-theory of the integers, namely that Kn(Z) = 0 whenever n is a multiple of 4 ... In fact from the

**Kummer–Vandiver conjecture**and the norm residue isomorphism theorem follow a full conjectural calculation of the K-groups for all values of n see Quillen–Lichtenbaum

**conjecture**for ...

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—Laurence Sterne (1713–1768)