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The constant pi, denoted pi, is a real number defined as the ratio of a circle's circumference C to its diameter d=2r, pi = C/d (1) = C/(2r) (2) pi has decimal expansion ...

Carmichael's conjecture asserts that there are an infinite number of Carmichael numbers. This was proven by Alford et al. (1994).

The central binomial coefficient (2n; n) is never squarefree for n>4. This was proved true for all sufficiently large n by Sárkőzy's theorem. Goetgheluck (1988) proved the ...

Also called the Tait flyping conjecture. Given two reduced alternating projections of the same knot, they are equivalent on the sphere iff they are related by a series of ...

The conjecture that all integers >1 occur as a value of the totient valence function (i.e., all integers >1 occur as multiplicities). The conjecture was proved by Ford ...

Let p be a non-wandering point of a diffeomorphism S:M->M of a compact manifold. The closing lemma concerns if S can be arbitrarily well approximated with derivatives of ...

A proposition which is consistent with known data, but has neither been verified nor shown to be false. It is synonymous with hypothesis.

The two-dimensional version of the ham sandwich theorem.

If a circular pizza is divided into 8, 12, 16, ... slices by making cuts at equal angles from an arbitrary point, then the sums of the areas of alternate slices are equal. ...

Consider n intersecting ellipses. The maximal number of regions into which these divide the plane are N(n)=2n^2-2n+2=2(n^2-n+1), giving values for n=1, 2, ... of 2, 6, 14, ...