(mathematics) A conjecture concerning the relationship between the locations of roots and critical points of a polynomial function of a complex variable. It states that for a polynomial f(z)=(z-r_1)⋯(z-r_n), qquad (n>2) with all roots r₁, ..., rₙ inside the closed unit disk |z| ≤ 1, each of the n roots is at a distance no more than 1 from at least one critical point.

(mathematics) Synonym of Sendov's conjecture

(number theory) The conjecture (disproved in 1958) that at least half of the natural numbers smaller than any given number have an odd number of prime factors.

(geometry) The conjecture that, in any tiling of n-dimensional Euclidean space by identical hypercubes, there are two hypercubes that share an entire (n − 1)-dimensional face with each other.

(mathematics, complex analysis) The theorem that if a complex number is a root for a polynomial with real coefficients, the complex conjugate of that number will also be a root.