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A number n is called k-hyperperfect if n = 1+ksum_(i)d_i (1) = 1+k[sigma(n)-n-1], (2) where sigma(n) is the divisor function and the summation is over the proper divisors ...

If two points A and A^' are inverse with respect to a circle (the inversion circle), then the straight line through A^' which is perpendicular to the line of the points AA^' ...

A collection of identities which hold on a Kähler manifold, also called the Hodge identities. Let omega be a Kähler form, d=partial+partial^_ be the exterior derivative, ...

C. Kimberling has extensively tabulated and enumerated the properties of triangle centers (Kimberling 1994, 1998, and online), denoting the nth center in his numbering scheme ...

A grand unified theory of mathematics which includes the search for a generalization of Artin reciprocity (known as Langlands reciprocity) to non-Abelian Galois extensions of ...

The appearance of nontrivial zeros (i.e., those along the critical strip with R[z]=1/2) of the Riemann zeta function zeta(z) very close together. An example is the pair of ...

Li's criterion states that the Riemann hypothesis is equivalent to the statement that, for lambda_n=1/((n-1)!)(d^n)/(ds^n)[s^(n-1)lnxi(s)]|_(s=1), (1) where xi(s) is the ...

There are two versions of the moat-crossing problem, one geometric and one algebraic. The geometric moat problems asks for the widest moat Rapunzel can cross to escape if she ...

A set n distinct numbers taken from the interval [1,n^2] form a magic series if their sum is the nth magic constant M_n=1/2n(n^2+1) (Kraitchik 1942, p. 143). If the sum of ...

The first theorem of Pappus states that the surface area S of a surface of revolution generated by the revolution of a curve about an external axis is equal to the product of ...