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The maximal irredundance polynomial R_G(x) for the graph G may be defined as the polynomial R_G(x)=sum_(k=ir(G))^(IR(G))r_kx^k, where ir(G) is the (lower) irredundance ...

The maximal matching-generating polynomial M_G(x) for the graph G may be defined as the polynomial M_G(x)=sum_(k=nu_L(G))^(nu(G))m_kx^k, where nu_L(G) is the lower matching ...

A sequence {mu_n}_(n=0)^infty is positive definite if the moment of every nonnegative polynomial which is not identically zero is greater than zero (Widder 1941, p. 132). ...

A formula for the number of Young tableaux associated with a given Ferrers diagram. In each box, write the sum of one plus the number of boxes horizontally to the right and ...

Any nondegenerate closed space curve may be nondegenerately deformed into either of the two curves illustrated above. Neither of these can be nondegenerately transformed into ...

A public-key cryptography algorithm which uses prime factorization as the trapdoor one-way function. Define n=pq (1) for p and q primes. Also define a private key d and a ...

Elementary methods consist of arithmetic, geometry, and high school algebra. These are the only tools that may be used in the branch of number theory known as elementary ...

The Fermat number F_n is prime iff 3^(2^(2^n-1))=-1 (mod F_n).

Smale's problems are a list of 18 challenging problems for the twenty-first century proposed by Field medalist Steven Smale. These problems were inspired in part by Hilbert's ...

Subtraction is the operation of taking the difference d=x-y of two numbers x and y. Here, x is called the minuend, y is called the subtrahend, and the symbol between the x ...