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A friend of a number n is another number m such that (m,n) is a friendly pair.

A friendly number is a number that is a member of a friendly pair or a higher-order friendly n-tuple. Numbers that are not friendly are said to be solitary. There are some ...

Define the abundancy Sigma(n) of a positive integer n as Sigma(n)=(sigma(n))/n, (1) where sigma(n) is the divisor function. Then a pair of distinct numbers (k,m) is a ...

There are seven frieze groups, which can be written in orbifold notation as *22infty, 2*infty, 22infty, *inftyinfty, infty*, inftyx, inftyinfty.

In general, a frieze consists of repeated copies of a single motif. b ; a d; c Conway and Guy (1996) define a frieze pattern as an arrangement of numbers at the intersection ...

The Fritsch graph is the 9-node planar graph illustrated above that tangles the Kempe chains in Kempe's algorithm and thus provides an example of how Kempe's supposed proof ...

Almost all natural numbers are very, very, very large (Steinbach 1990, p. 111).

The permanent of an n×n integer matrix with all entries either 0 or 1 is 0 iff the matrix contains an r×s submatrix of 0s with r+s=n+1. This result follows from the ...

rho_(n+1)(x)=intrho_n(y)delta[x-M(y)]dy, where delta(x) is a delta function, M(x) is a map, and rho is the natural invariant.

Let F be a field of field characteristic p. Then the Frobenius automorphism on F is the map phi:F->F which maps alpha to alpha^p for each element alpha of F.