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A prime factorization algorithm which can be implemented in a single-step or double-step form. In the single-step version, a prime factor p of a number n can be found if p-1 ...

A radical integer is a number obtained by closing the integers under addition, multiplication, subtraction, and root extraction. An example of such a number is RadicalBox[7, ...

A repunit prime is a repunit (i.e., a number consisting of copies of the single digit 1) that is also a prime number. The base-10 repunit (possibly probable) primes ...

Rubik's Clock is a puzzle consisting of 18 small clocks, 14 of which are independent, each of which may be set to any 12-hour position. There are therefore 12^(14) possible ...

A partition whose conjugate partition is equivalent to itself. The Ferrers diagrams corresponding to the self-conjugate partitions for 3<=n<=10 are illustrated above. The ...

Let U(P,Q) and V(P,Q) be Lucas sequences generated by P and Q, and define D=P^2-4Q. (1) Let n be an odd composite number with (n,D)=1, and n-(D/n)=2^sd with d odd and s>=0, ...

A weakly perfect graph is a graph for which omega(G)=chi(G) (without any requirement that this condition also hold on induced subgraphs, which is required for a graph to be ...

Van der Corput sequences are a means of generating sequences of points that are maximally self-avoiding (a.k.a. quasirandom sequences). In the one-dimensional case, the ...

Given a point set P={x_n}_(n=0)^(N-1) in the s-dimensional unit cube [0,1)^s, the star discrepancy is defined as D_N^*(P)=sup_(J in Upsilon^*)D(J,P), (1) where the local ...

Let U(P,Q) and V(P,Q) be Lucas sequences generated by P and Q, and define D=P^2-4Q. (1) Then {U_((n-(D/n))/2)=0 (mod n) when (Q/n)=1; V_((n-(D/n))/2)=D (mod n) when (Q/n)=-1, ...