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Consider an n-digit number k. Square it and add the right n digits to the left n or n-1 digits. If the resultant sum is k, then k is called a Kaprekar number. For example, 9 ...

The Labs septic is a septic surface having 99 ordinary double points, which is the maximum number known for any septic surface.

For n>=1, let u and v be integers with u>v>0 such that the Euclidean algorithm applied to u and v requires exactly n division steps and such that u is as small as possible ...

If K is a finite complex and h:|K|->|K| is a continuous map, then Lambda(h)=sum(-1)^pTr(h_*,H_p(K)/T_p(K)) is the Lefschetz number of the map h.

A type of diagram invented by Lewis Carroll (the name is an abbreviation of "Lewis") that can be used to determine the number of minimal covers of n numbers with k members.

Given a point set P={x_n}_(n=0)^(N-1) in the s-dimensional unit cube [0,1)^s, the local discrepancy is defined as D(J,P)=|(number of x_n in J)/N-Vol(J)|, Vol(J) is the ...

Data resulting from the observation of a population on a number of variables over time. Whenever observations are made more than once, the data is considered to be ...

The lower independence number i(G) of a graph G is the minimum size of a maximal independent vertex set in G. The lower indepedence number is equiavlent to the "independent ...

There are several types of numbers that are commonly termed "lucky numbers." The first is the lucky numbers of Euler. The second is obtained by writing out all odd numbers: ...

For a real number x, the mantissa is defined as the positive fractional part x-|_x_|=frac(x), where |_x_| denotes the floor function. For example, for x=3.14159, the mantissa ...