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Relates invariants of a curve defined over the integers. If this inequality were proven true, then Fermat's last theorem would follow for sufficiently large exponents. ...

The Ramsey number R(m,n) gives the solution to the party problem, which asks the minimum number of guests R(m,n) that must be invited so that at least m will know each other ...

A Carmichael number is an odd composite number n which satisfies Fermat's little theorem a^(n-1)-1=0 (mod n) (1) for every choice of a satisfying (a,n)=1 (i.e., a and n are ...

The Riemann zeta function is an extremely important special function of mathematics and physics that arises in definite integration and is intimately related with very deep ...

The partial order width of a set P is equal to the minimum number of chains needed to cover P. Equivalently, if a set P of ab+1 elements is partially ordered, then P contains ...

Let a^p+b^p=c^p be a solution to Fermat's last theorem. Then the corresponding Frey curve is y^2=x(x-a^p)(x+b^p). (1) Ribet (1990a) showed that such curves cannot be modular, ...

A matrix whose entries are all integers. Special cases which arise frequently are those having only (-1,1) as entries (e.g., Hadamard matrix), (0,1)-matrices having only ...

Let A be a matrix and x and b vectors. Then the system Ax=b, x>=0 has no solution iff the system A^(T)y>=0, b^(T)y<0 has a solution, where y is a vector (Fang and Puthenpura ...

The correspondence which relates the Hanoi graph to the isomorphic graph of the odd binomial coefficients in Pascal's triangle, where the adjacencies are determined by ...

A collection of moves together with a corresponding set of weights which are followed probabilistically in the playing of a game. The minimax theorem of game theory states ...