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Determination of whether predicate P(x_1,...,x_n) is true or false for any given values of x_1, ..., x_n is called its decision problem. The decision problem for predicate ...

A triangle is a 3-sided polygon sometimes (but not very commonly) called the trigon. Every triangle has three sides and three angles, some of which may be the same. The sides ...

A special case of the quadratic Diophantine equation having the form x^2-Dy^2=1, (1) where D>0 is a nonsquare natural number (Dickson 2005). The equation x^2-Dy^2=+/-4 (2) ...

If f is continuous on a closed interval [a,b], then there is at least one number x^* in [a,b] such that int_a^bf(x)dx=f(x^*)(b-a). The average value of the function (f^_) on ...

Two open manifolds M and M^' are cobordant if there exists a manifold with boundary W^(n+1) such that an acceptable restrictive relationship holds.

The American Mathematical Society awards two prizes named in honor of Prof. Frank Nelson Cole, a senior member of the AMS who made a bequest to the society in 1928 upon his ...

The conic sections are the nondegenerate curves generated by the intersections of a plane with one or two nappes of a cone. For a plane perpendicular to the axis of the cone, ...

An immediate consequence of a result already proved. Corollaries usually state more complicated theorems in a language simpler to use and apply.

A cubic curve is an algebraic curve of curve order 3. An algebraic curve over a field K is an equation f(X,Y)=0, where f(X,Y) is a polynomial in X and Y with coefficients in ...

If q is logically deducible from p, this is written p|-q.