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The Littlewood conjecture states that for any two real numbers x,y in R, lim inf_(n->infty)n|nx-nint(nx)||ny-nint(ny)|=0 where nint(z) denotes the nearest integer function. ...

The Markström graph is a cubic planar graph on 24 vertices which lacks cycles of length 4 and 8 but contains cycles of length 16. (In particular, it contains cycles of ...

Consider the average volume of a tetrahedron picked at random inside an octahedron of unit volume. The answer is difficult to compute analytically (Zinani 2003), but the mean ...

Let two disks of radius r intersect one another perpendicularly and have a diameter in common. If the distance between the centers of the disks is sqrt(2) times their radius, ...

Define the harmonic mean of the divisors of n H(n)=(sigma_0(n))/(sum_(d|n)1/d), where sigma_0(n) is the divisor function (the number of divisors of n). For n=1, 2, ..., the ...

If P(z) is a power series which is regular for |z|<=1 except for m poles within this circle and except for z=+1, at which points the function is assumed continuous when only ...

Apply the 196-algorithm, which consists of taking any positive integer of two digits or more, reversing the digits, and adding to the original number. Now sum the two and ...

The conjecture due to Pollock (1850) that every number is the sum of at most five tetrahedral numbers (Dickson 2005, p. 23; incorrectly described as "pyramidal numbers" and ...

A quartic nonhamiltonian graph is a quartic graph that is nonhamiltonian. A number of such graphs are illustrated above. Van Cleemput and Zamfirescu (2018) gave a 39-vertex ...

Let lambda_1, ..., lambda_n in C be linearly independent over the rationals Q, then Q(lambda_1,...,lambda_n,e^(lambda_1),...,e^(lambda_n)) has transcendence degree at least n ...