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A number n is called equidigital if the number of digits in the prime factorization of n (including powers) uses the same number of digits as the number of digits in n. The ...

A quadrilateral in which a pair of opposite sides have the same length and are inclined at 60 degrees to each other (or equivalently, satisfy <A>+<B>=120 degrees). Some ...

Two metrics g_1 and g_2 defined on a space X are called equivalent if they induce the same metric topology on X. This is the case iff, for every point x_0 of X, every ball ...

For |z|<1, product_(k=1)^infty(1+z^k)=product_(k=1)^infty(1-z^(2k-1))^(-1). (1) Both of these have closed form representation 1/2(-1;z)_infty, (2) where (a;q)_infty is a ...

The sum over all external (square) nodes of the lengths of the paths from the root of an extended binary tree to each node. For example, in the tree above, the external path ...

A subset F subset R of the real numbers is said to be an F_sigma set provided F is the countable union of closed sets. The name F_sigma comes from French: The F stands for ...

Fractran is an algorithm applied to a given list f_1, f_2, ..., f_k of fractions. Given a starting integer N, the FRACTRAN algorithm proceeds by repeatedly multiplying the ...

In a given acute triangle DeltaABC, find the inscribed triangle whose perimeter is as small as possible. The answer is the orthic triangle of DeltaABC. The problem was ...

Let T_n(x) be an arbitrary trigonometric polynomial T_n(x)=1/2a_0+{sum_(k=1)^n[a_kcos(kx)+b_ksin(kx)]} (1) with real coefficients, let f be a function that is integrable over ...

Fermat's sandwich theorem states that 26 is the only number sandwiched between a perfect square number (5^2=25) and a perfect cubic number (3^3=27). According to Singh ...