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Let B_k be the kth Bernoulli number and consider nB_(n-1)=-1 (mod n), where the residues of fractions are taken in the usual way so as to yield integers, for which the ...

The bellows conjecture asserts that all flexible polyhedra keep a constant volume as they are flexed (Cromwell 1997). The conjecture was apparently proposed by Dennis ...

A pair of vertices (x,y) of a graph G is called an omega-critical pair if omega(G+xy)>omega(G), where G+xy denotes the graph obtained by adding the edge xy to G and omega(H) ...

Carmichael's conjecture asserts that there are an infinite number of Carmichael numbers. This was proven by Alford et al. (1994).

Based on a problem in particle physics, Dyson (1962abc) conjectured that the constant term in the Laurent series product_(1<=i!=j<=n)(1-(x_i)/(x_j))^(a_i) is the multinomial ...

The Hadwiger conjecture is a generalization of the four-color theorem which states that for any loopless graph G with h(G) the Hadwiger number and chi(G) the chromatic ...

Let the minimal length of an addition chain for a number n be denoted l(n). Then the Scholz conjecture, also called the Scholz-Brauer conjecture or Brauer-Scholz conjecture, ...

The conjecture that all integers >1 occur as a value of the totient valence function (i.e., all integers >1 occur as multiplicities). The conjecture was proved by Ford ...

Keller conjectured that tiling an n-dimensional space with n-dimensional hypercubes of equal size yields an arrangement in which at least two hypercubes have an entire ...

Given the Mertens function defined by M(n)=sum_(k=1)^nmu(k), (1) where mu(n) is the Möbius function, Stieltjes claimed in an 1885 letter to Hermite that M(x)x^(-1/2) stays ...