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A spectrum sequence is a sequence formed by successive multiples of a real number a rounded down to the nearest integer s_n=|_na_|. If a is irrational, the spectrum is called ...

A Poulet number whose divisors d all satisfy d|2^d-2. The first few are 341, 1387, 2047, 2701, 3277, 4033, 4369, 4681, 5461, 7957, 8321, ... (OEIS A050217).

A set of circuits going along the graph edges of a graph, each with an even number of graph edges, such that just one of the circuits passes through each graph vertex (Ball ...

1000=10^3. The word "thousand" appears in common expressions in a number of languages, for example, "a thousand pardons" in English and "tusen takk" ("a thousand thanks") in ...

Every real number is negative, 0, or positive. The law is sometimes stated as "For arbitrary real numbers a and b, exactly one of the relations a<b, a=b, a>b holds" (Apostol ...

A two-graph (V,Delta) on nodes V is a collection Delta of unordered triples of the vertices (the so-called "odd triples") such that each 4-tuple of V contains an even number ...

The depth of a vertex v in a rooted tree as the number of edges from v to the root vertex. A function to return the depth of a vertex v in a tree g may be implemented in a ...

On an algebraic curve, the sum of the number of coincidences at a noncuspidal point C is the sum of the orders of the infinitesimal distances from a nearby point P to the ...

If there is a (nu,nu^') correspondence between two curves of curve genus p and p^' and the number of branch points properly counted are beta and beta^', then ...

Diagonalize a form over the rationals to diag[p^a·A,p^b·B,...], where all the entries are integers and A, B, ... are relatively prime to p. Then the p-signature of the form ...