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A symmetric block design (4n+3, 2n+1, n) which is equivalent to a Hadamard matrix of order 4n+4. It is conjectured that Hadamard designs exist for all integers n>0, but this ...

The Higman-Sims group is the sporadic group HS of order |HS| = 44352000 (1) = 2^9·3^2·5^3·7·11. (2) The Higman-Sims group is 2-transitive, and has permutation representations ...

A number triangle of order n with entries 1 to n such that entries are nondecreasing across rows and down columns and all entries in column j are less than or equal to j. An ...

Let sigma_0(n) and sigma_1(n) denote the number and sum of the divisors of n, respectively (i.e., the zeroth- and first-order divisor functions). A number n is called sublime ...

Let {f_n(x)} be a sequence of analytic functions regular in a region G, and let this sequence be uniformly convergent in every closed subset of G. If the analytic function ...

z(1-z)(d^2y)/(dz^2)+[c-(a+b+1)z](dy)/(dz)-aby=0. It has regular singular points at 0, 1, and infty. Every second-order ordinary differential equation with at most three ...

A second-order partial differential equation arising in physics, del ^2psi=-4pirho. If rho=0, it reduces to Laplace's equation. It is also related to the Helmholtz ...

A powerful numerical integration technique which uses k refinements of the extended trapezoidal rule to remove error terms less than order O(N^(-2k)). The routine advocated ...

A multimagic square such that the first, second, third, and fourth powers of the elements all yield magic squares is known as a tetramagic square. The first known tetramagic ...

A pair of primes (p,q) that sum to an even integer 2n=p+q are known as a Goldbach partition (Oliveira e Silva). Letting r(2n) denote the number of Goldbach partitions of 2n ...