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A proof which can be accomplished using only real numbers (i.e., real analysis instead of complex analysis; Hoffman 1998, pp. 92-93).

Suppose a,b in N, n=ab+1, and x_1, ..., x_n is a sequence of n real numbers. Then this sequence contains a monotonic increasing (decreasing) subsequence of a+1 terms or a ...

A factorial prime is a prime number of the form n!+/-1, where n! is a factorial. n!-1 is prime for n=3, 4, 6, 7, 12, 14, 30, 32, 33, 38, 94, 166, 324, 379, 469, 546, 974, ...

Numbers 1, alpha_1, ..., alpha_L are rationally independent iff under the action of rotation rho_(alpha_1)×...×rho_(alpha_L) on the L-dimensional torus, every orbit is ...

The method of exhaustion was an integral-like limiting process used by Archimedes to compute the area and volume of two-dimensional lamina and three-dimensional solids.

Maximize the amount of floor space which can be covered with a fixed tile (Hoffman 1998, p. 173).

The term "continued fraction" is used to refer to a class of expressions of which generalized continued fraction of the form b_0+(a_1)/(b_1+(a_2)/(b_2+(a_3)/(b_3+...))) ...

A problem is assigned to the NP (nondeterministic polynomial time) class if it is solvable in polynomial time by a nondeterministic Turing machine. A P-problem (whose ...

A Woodall prime is a Woodall number W_n=2^nn-1 that is prime. The first few Woodall primes are 7, 23, 383, 32212254719, 2833419889721787128217599, ... (OEIS A050918), ...

A Hamiltonian path, also called a Hamilton path, is a graph path between two vertices of a graph that visits each vertex exactly once. If a Hamiltonian path exists whose ...