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There are two versions of the moat-crossing problem, one geometric and one algebraic. The geometric moat problems asks for the widest moat Rapunzel can cross to escape if she ...

Informally, a function f is a one-way function if 1. The description of f is publicly known and does not require any secret information for its operation. 2. Given x, it is ...

Odd values of Q(n) are 1, 1, 3, 5, 27, 89, 165, 585, ... (OEIS A051044), and occur with ever decreasing frequency as n becomes large (unlike P(n), for which the fraction of ...

A pseudoperfect number, sometimes also called a semiperfect number (Benkoski 1972, Butske et al. 1999), is a positive integer such as 20=1+4+5+10 which is the sum of some (or ...

If p and q are distinct odd primes, then the quadratic reciprocity theorem states that the congruences x^2=q (mod p) x^2=p (mod q) (1) are both solvable or both unsolvable ...

The constant s_0 in Schnirelmann's theorem such that every integer >1 is a sum of at most s_0 primes. Of course, by Vinogradov's theorem, it is known that 4 primes suffice ...

A divisor d of n for which GCD(d,n/d)=1, (1) where GCD(m,n) is the greatest common divisor. For example, the divisors of 12 are {1,2,3,4,6,12}, so the unitary divisors are ...

The volume of a solid body is the amount of "space" it occupies. Volume has units of length cubed (i.e., cm^3, m^3, in^3, etc.) For example, the volume of a box (cuboid) of ...

The triangular number T_n is a figurate number that can be represented in the form of a triangular grid of points where the first row contains a single element and each ...

In mathematics, a knot is defined as a closed, non-self-intersecting curve that is embedded in three dimensions and cannot be untangled to produce a simple loop (i.e., the ...