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An extension of the secant method of root finding to higher dimensions.

The Burnside problem originated with Burnside (1902), who wrote, "A still undecided point in the theory of discontinuous groups is whether the group order of a group may be ...

A Mandelbrot set-like fractal obtained by iterating the map z_(n+1)=z_n^3+(z_0-1)z_n-z_0.

The partial differential equation u_(xxx)-1/8u_x^3+u_x(Ae^u+Be^(-u))=0.

Each point in the convex hull of a set S in R^n is in the convex combination of n+1 or fewer points of S.

A Carmichael number is an odd composite number n which satisfies Fermat's little theorem a^(n-1)-1=0 (mod n) (1) for every choice of a satisfying (a,n)=1 (i.e., a and n are ...

The relationship Sq^i(x cup y)=Sigma_(j+k=i)Sq^j(x) cup Sq^k(y) encountered in the definition of the steenrod algebra.

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 ...

Let t be a nonnegative integer and let x_1, ..., x_t be nonzero elements of Z_p which are not necessarily distinct. Then the number of elements of Z_p that can be written as ...

If (1-z)^(a+b-c)_2F_1(2a,2b;2c;z)=sum_(n=0)^inftya_nz^n, then where (a)_n is a Pochhammer symbol and _2F_1(a,b;c;z) is a hypergeometric function.