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A short theorem used in proving a larger theorem. Related concepts are the axiom, porism, postulate, principle, and theorem. The late mathematician P. Erdős has often been ...

Every odd integer n is a prime or the sum of three primes. This problem is closely related to Vinogradov's theorem.

If the first case of Fermat's last theorem is false for the prime exponent p, then 3^(p-1)=1 (mod p^2).

A specific type of ultraproduct that can be used to construct nonstandard universes and obtain the transfer principle as a corollary of Łoś' theorem for ultraproducts.

A closed interval is an interval that includes all of its limit points. If the endpoints of the interval are finite numbers a and b, then the interval {x:a<=x<=b} is denoted ...

A function f(x) is said to be concave on an interval [a,b] if, for any points x_1 and x_2 in [a,b], the function -f(x) is convex on that interval (Gradshteyn and Ryzhik 2000).

A point of discontinuity, also called a leap.

A function or curve is piecewise continuous if it is continuous on all but a finite number of points at which certain matching conditions are sometimes required.

The 10_3 configuration of ten lines intersecting three at a time in 10 points which arises in Desargues' theorem. Its Levi graph is the Desargues graph.

The Diophantine equation x^n+y^n=z^n. The assertion that this equation has no nontrivial solutions for n>2 has a long and fascinating history and is known as Fermat's last ...