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High Quality Content by WIKIPEDIA articles! In mathematics, Vandiver's conjecture concerns a property of algebraic number fields. Although attributed to American mathematician Harry Vandiver, the conjecture was first made in a letter from Ernst Kummer to Leopold Kronecker. Let K=mathbb{Q}(zeta_p)^+, the maximal real subfield of the p-th cyclotomic field. Vandiver's conjecture states that p does not divide hK, the class number of K. For comparison, see the entry on regular and irregular primes.