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Define a carefree couple as a pair of positive integers (a,b) such that a and b are relatively prime (i.e., GCD(a,b)=1) and a is squarefree. Similarly, define a strongly ...

A game in which each player has a finite number of moves and a finite number of choices at each move.

B_(p+k)=B_k+B_(k+1) (mod p), when p is prime and B_n is a Bell number.

An integer used to generate a digitaddition. A number can have more than one generator. If a number has no generator, it is called a self number.

In any tree, the number of dissimilar points minus the number of dissimilar lines plus the number of symmetry lines equals 1.

Given a number n, Fermat's factorization methods look for integers x and y such that n=x^2-y^2. Then n=(x-y)(x+y) (1) and n is factored. A modified form of this observation ...

A puzzle in which one object is to be converted to another by making a finite number of cuts and reassembling it. The cuts are often, but not always, restricted to straight ...

For a quadratic form Q in the canonical form Q=y_1^2+y_2^2+...+y_p^2-y_(p+1)^2-y_(p+2)^2-...-y_r^2, the rank is the total number r of square terms (both positive and ...

The companion matrix to a monic polynomial a(x)=a_0+a_1x+...+a_(n-1)x^(n-1)+x^n (1) is the n×n square matrix A=[0 0 ... 0 -a_0; 1 0 ... 0 -a_1; 0 1 ... 0 -a_2; | | ... ... |; ...

A groupoid S such that for all a,b in S, there exist unique x,y in S such that ax = b (1) ya = b. (2) No other restrictions are applied; thus a quasigroup need not have an ...