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A prime p_n is called "good" if p_n^2>p_(n-i)p_(n+i) for all 1<=i<=n-1 (there is a typo in Guy 1994 in which the is are replaced by 1s). There are infinitely many good ...

The assignment of labels or colors to the edges or vertices of a graph. The most common types of graph colorings are edge coloring and vertex coloring.

A connected labeled graph with n graph edges in which all graph vertices can be labeled with distinct integers (mod n) so that the sums of the pairs of numbers at the ends of ...

The Hermite constant is defined for dimension n as the value gamma_n=(sup_(f)min_(x_i)f(x_1,x_2,...,x_n))/([discriminant(f)]^(1/n)) (1) (Le Lionnais 1983). In other words, ...

The term isocline derives from the Greek words for "same slope." For a first-order ordinary differential equation y^'=f(t,y) is, a curve with equation f(t,y)=C for some ...

The term "lobster" is used to refer either to a particular polyiamond or to a class of tree called a lobster graph. When referring to polyiamonds, the lobster is the ...

Is it possible to cover completely the surface of a sphere with congruent, nonoverlapping arcs of great circles? Conway and Croft (1964) proved that it can be covered with ...

There exist lattices in n dimensions having hypersphere packing densities satisfying eta>=(zeta(n))/(2^(n-1)), where zeta(n) is the Riemann zeta function. However, the proof ...

What is the longest ladder that can be moved around a right-angled hallway of unit width? For a straight, rigid ladder, the answer is 2sqrt(2), which allows the ladder to ...

The number of multisets of length k on n symbols is sometimes termed "n multichoose k," denoted ((n; k)) by analogy with the binomial coefficient (n; k). n multichoose k is ...