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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 ...

A Moore graph of type (v,g) is a regular graph of vertex degree v>2 and girth g that contains the maximum possible number of nodes, namely ...

A (k,l)-multigrade equation is a Diophantine equation of the form sum_(i=1)^ln_i^j=sum_(i=1)^lm_i^j (1) for j=1, ..., k, where m and n are l-vectors. Multigrade identities ...

Starting with the circle P_1 tangent to the three semicircles forming the arbelos, construct a chain of tangent circles P_i, all tangent to one of the two small interior ...

A primality test is a test to determine whether or not a given number is prime, as opposed to actually decomposing the number into its constituent prime factors (which is ...

A self-avoiding walk is a path from one point to another which never intersects itself. Such paths are usually considered to occur on lattices, so that steps are only allowed ...

The term "square" can be used to mean either a square number ("x^2 is the square of x") or a geometric figure consisting of a convex quadrilateral with sides of equal length ...

A number which is simultaneously square and triangular. Let T_n denote the nth triangular number and S_m the mth square number, then a number which is both triangular and ...

Thurston's conjecture proposed a complete characterization of geometric structures on three-dimensional manifolds. Before stating Thurston's geometrization conjecture in ...

A Turing machine is a theoretical computing machine invented by Alan Turing (1937) to serve as an idealized model for mathematical calculation. A Turing machine consists of a ...