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The Fermat quotient for a number a and a prime base p is defined as q_p(a)=(a^(p-1)-1)/p. (1) If pab, then q_p(ab) = q_p(a)+q_p(b) (2) q_p(p+/-1) = ∓1 (3) (mod p), where the ...

For any sequence of integers 0<n_1<...<n_k, there is a flag manifold of type (n_1, ..., n_k) which is the collection of ordered sets of vector subspaces of R^(n_k) (V_1, ..., ...

Also called the Tait flyping conjecture. Given two reduced alternating projections of the same knot, they are equivalent on the sphere iff they are related by a series of ...

Consider the forms Q for which the generic characters chi_i(Q) are equal to some preassigned array of signs e_i=1 or -1, e_1,e_2,...,e_r, subject to product_(i=1)^(r)e_i=1. ...

A subset G subset R of the real numbers is said to be a G_delta set provided G is the countable intersection of open sets. The name G_delta comes from German: The G stands ...

The upper central series of a group G is the sequence of groups (each term normal in the term following it) 1=Z_0<=Z_1<=Z_2<=...<=Z_n<=... that is constructed in the ...

Given a number field K, there exists a unique maximal unramified Abelian extension L of K which contains all other unramified Abelian extensions of K. This finite field ...

The Gelfond-Schneider constant is sometimes known as the Hilbert number. Flannery and Flannery (2000, p. 35) define a Hilbert number as a positive integer of the form n=4k+1 ...

Honaker's problem asks for all consecutive prime number triples (p,q,r) with p<q<r such that p|(qr+1). Caldwell and Cheng (2005) showed that the only Honaker triplets for ...

An ordinal number is called an initial ordinal if every smaller ordinal has a smaller cardinal number (Moore 1982, p. 248; Rubin 1967, p. 271). The omega_alphas ordinal ...