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A geodesic dome is a triangulation of a Platonic solid or other polyhedron to produce a close approximation to a sphere (or hemisphere). The nth order geodesation operation ...

Let there be n ways for a "good" selection and m ways for a "bad" selection out of a total of n+m possibilities. Take N samples and let x_i equal 1 if selection i is ...

A generalization of the p-adic norm first proposed by Kürschák in 1913. A valuation |·| on a field K is a function from K to the real numbers R such that the following ...

Find consecutive powers, i.e., solutions to x^p-y^q=+/-1, excluding 0 and 1. Catalan's conjecture states that the only solution is 3^2-2^3=1, so 8 and 9 (2^3 and 3^2) are the ...

A metric characterizing the difference between two knots K and K^' in S^3.

The partial differential equation u_(tt)-u_(xx)-u+u^3=0.

The partial differential equation u_(tt)-u_(xx)=epsilon(u_t-u_t^3).

Let S(x) denote the number of positive integers not exceeding x which can be expressed as a sum of two squares (i.e., those n<=x such that the sum of squares function ...

Primorial primes are primes of the form p_n#+/-1, where p_n# is the primorial of p_n. A coordinated search for such primes is being conducted on PrimeGrid. p_n#-1 is prime ...

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 ...