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Consider h_+(d) proper equivalence classes of forms with discriminant d equal to the field discriminant, then they can be subdivided equally into 2^(r-1) genera of ...

Let S(T) be the group of symmetries which map a monohedral tiling T onto itself. The transitivity class of a given tile T is then the collection of all tiles to which T can ...

If f_1(x), ..., f_s(x) are irreducible polynomials with integer coefficients such that no integer n>1 divides f_1(x), ..., f_s(x) for all integers x, then there should exist ...

The maximal number of regions into which space can be divided by n planes is f(n)=1/6(n^3+5n+6) (Yaglom and Yaglom 1987, pp. 102-106). For n=1, 2, ..., these give the values ...

A pseudoprime which obeys an additional restriction beyond that required for a Frobenius pseudoprime. A number n with (n,2a)=1 is a strong Frobenius pseudoprime with respect ...

A brute-force method of finding a divisor of an integer n by simply plugging in one or a set of integers and seeing if they divide n. Repeated application of trial division ...

A p-adic integer is a p-adic number of the form sum_(k=m)^(infty)a_kp^k, where m>=0, a_k are integers, and p is prime. It is sufficient to take a_k in the set {0,1,...,p-1}. ...

In general, polynomial equations higher than fourth degree are incapable of algebraic solution in terms of a finite number of additions, subtractions, multiplications, ...

The Farey sequence F_n for any positive integer n is the set of irreducible rational numbers a/b with 0<=a<=b<=n and (a,b)=1 arranged in increasing order. The first few are ...

In the theory of transfinite ordinal numbers, 1. Every well ordered set has a unique ordinal number, 2. Every segment of ordinals (i.e., any set of ordinals arranged in ...