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Legendre's formula counts the number of positive integers less than or equal to a number x which are not divisible by any of the first a primes, (1) where |_x_| is the floor ...

The Leonard graph is a distance-regular graph on 288 vertices (Brouwer et al. 1989, p. 369) with intersection array {12,11,10,7;1,2,5,12}. It is however not ...

Levy (1963) noted that 13 = 3+(2×5) (1) 19 = 5+(2×7), (2) and from this observation, conjectured that all odd numbers >=7 are the sum of a prime plus twice a prime. This ...

The study of number fields by embedding them in a local field is called local class field theory. Information about an equation in a local field may give information about ...

A topological space X is locally compact if every point has a neighborhood which is itself contained in a compact set. Many familiar topological spaces are locally compact, ...

Lucas's theorem states that if n>=3 be a squarefree integer and Phi_n(z) a cyclotomic polynomial, then Phi_n(z)=U_n^2(z)-(-1)^((n-1)/2)nzV_n^2(z), (1) where U_n(z) and V_n(z) ...

Minesweeper is single-player logic-based computer game played on rectangular board whose object is to locate a predetermined number of randomly-placed "mines" in the shortest ...

Let a in C and |a|<1, then phi_a(z)=(z-a)/(1-a^_z) is a Möbius transformation, where a^_ is the complex conjugate of a. phi_a is a conformal mapping self-map of the unit disk ...

Let E be the largest and e the smallest power of l in the HOMFLY polynomial of an oriented link, and i be the braid index. Then the Morton-Franks-Williams inequality holds, ...

Call a number of the form n^2-k a "near-square number." Numbers of the form n^2-5 for n=1, 2, ... are -4, -1, 4, 11, 20, 31, 44, 59, 76, 95, ... (OEIS A028875). These are ...