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Every odd integer n is a prime or the sum of three primes. This problem is closely related to Vinogradov's theorem.

Euler conjectured that at least n nth powers are required for n>2 to provide a sum that is itself an nth power. The conjecture was disproved by Lander and Parkin (1967) with ...

Macdonald's constant term conjectures are related to root systems of Lie algebras (Macdonald 1982, Andrews 1986). They can be regarded as generalizations of Dyson's ...

Macdonald's plane partition conjecture proposes a formula for the number of cyclically symmetric plane partitions (CSPPs) of a given integer whose Ferrers diagrams fit inside ...

Montgomery's pair correlation conjecture, published in 1973, asserts that the two-point correlation function R_2(r) for the zeros of the Riemann zeta function zeta(z) on the ...

Euler conjectured that there do not exist Euler squares of order n=4k+2 for k=1, 2, .... In fact, MacNeish (1921-1922) published a purported proof of this conjecture (Bruck ...

The Ablowitz-Ramani-Segur conjecture states that a nonlinear partial differential equation is solvable by the inverse scattering method only if every nonlinear ordinary ...

In his monumental treatise Disquisitiones Arithmeticae, Gauss conjectured that the class number h(-d) of an imaginary quadratic field with binary quadratic form discriminant ...

Tait's Hamiltonian graph conjecture asserted that every cubic polyhedral graph is Hamiltonian. It was proposed by Tait in 1880 and refuted by Tutte (1946) with a ...

Informally, an elliptic curve is a type of cubic curve whose solutions are confined to a region of space that is topologically equivalent to a torus. The Weierstrass elliptic ...