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A set A of integers is productive if there exists a partial recursive function f such that, for any x, the following holds: If the domain of phi_x is a subset of A, then f(x) ...

If the integral coefficients C_0, C_1, ..., C_(N-1) of the polynomial f(x)=C_0+C_1x+C_2x^2+...+C_(N-1)x^(N-1)+x^N are divisible by a prime number p, while the free term C_0 ...

Given a set P with |P|=p elements consisting of c_1 numbers 1, c_2 numbers 2, ..., and c_n numbers n and c_1+c_2+...+c_n=p, find the number of permutations with k-1 rises ...

Let gamma(G) denote the domination number of a simple graph G. Then Vizing (1963) conjectured that gamma(G)gamma(H)<=gamma(G×H), where G×H is the graph product. While 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 ...

Given any assignment of n-element sets to the n^2 locations of a square n×n array, is it always possible to find a partial Latin square? The fact that such a partial Latin ...

Polysticks, sometimes also known as polyedges, are polyforms obtained from the edges of a regular grid. Square polysticks are polyforms obtained from the edges of a regular ...

Decimal is the base-10 notational system for representing real numbers. The expression of a number using the decimal system is called its decimal expansion, examples of which ...

The fibonomial coefficient (sometimes also called simply the Fibonacci coefficient) is defined by [m; k]_F=(F_mF_(m-1)...F_(m-k+1))/(F_1F_2...F_k), (1) where [m; 0]_F=1 and ...

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 ...