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Consider the Fibonacci-like recurrence a_n=+/-a_(n-1)+/-a_(n-2), (1) where a_0=0, a_1=1, and each sign is chosen independently and at random with probability 1/2. ...

The Seidel-Entringer-Arnold triangle is the number triangle consisting of the Entringer numbers E_(n,k) arranged in "ox-plowing" order, ...

The Whittaker functions arise as solutions to the Whittaker differential equation. The linearly independent solutions to this equation are M_(k,m)(z) = ...

Carmichael's conjecture asserts that there are an infinite number of Carmichael numbers. This was proven by Alford et al. (1994).

The central binomial coefficient (2n; n) is never squarefree for n>4. This was proved true for all sufficiently large n by Sárkőzy's theorem. Goetgheluck (1988) proved the ...

A block matrix is a matrix that is defined using smaller matrices, called blocks. For example, [A B; C D], (1) where A, B, C, and D are themselves matrices, is a block ...

An algebraic variety is called irreducible if it cannot be written as the union of nonempty algebraic varieties. For example, the set of solutions to xy=0 is reducible ...

A function f(x) satisfies the Lipschitz condition of order beta at x=0 if |f(h)-f(0)|<=B|h|^beta for all |h|<epsilon, where B and beta are independent of h, beta>0, and alpha ...

An infinite sequence {a_i} of positive integers is called strongly independent if any relation sumepsilon_ia_i, with epsilon_i=0, +/-1, or +/-2 and epsilon_i=0 except ...

An infinite sequence {a_i} of positive integers is called weakly independent if any relation sumepsilon_ia_i with epsilon_i=0 or +/-1 and epsilon_i=0, except finitely often, ...