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In 1891, Chebyshev and Sylvester showed that for sufficiently large x, there exists at least one prime number p satisfying x<p<(1+alpha)x, where alpha=0.092.... Since the ...

A proof which can be accomplished using only real numbers (i.e., real analysis instead of complex analysis; Hoffman 1998, pp. 92-93).

The problem of determining (or counting) the set of all solutions to a given problem.

The question of whether a solution to a given problem exists. The existence problem can be solved in the affirmative without actually finding a solution to the original ...

A congruence of the form f(x)=g(x) (mod n), where f(x) and g(x) are both integer polynomials. Functional congruences are sometimes also called "identical congruences" (Nagell ...

A list of problems in low-dimensional topology maintained by Kirby (1995). The list currently runs about 380 pages.

Let K be a finite complex, let h:|K|->|K| be a continuous map. If Lambda(h)!=0, then h has a fixed point.

The line bisecting a given line segment P_1P_2 can be constructed geometrically, as illustrated above.

The result of a matrix multiplication.

A multiplicand is a quantity that is multiplied by another (the multiplier). For example, in the expression a×b, b is the multiplicand. The result of the multiplication of ...