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An NSW number (named after Newman, Shanks, and Williams) is an integer m that solves the Diophantine equation 2n^2=m^2+1. (1) In other words, the NSW numbers m index the ...

A number which can be represented both in the form x_0^2-Dy_0^2 and in the form Dx_1^2-y_1^2. This is only possible when the Pell equation x^2-Dy^2=-1 (1) is solvable. Then ...

The asterisk *, also called a "star," is used for a number of different purposed in mathematics. The most common usage is to denote multiplication so, for example, 2*3=2×3=6. ...

A transformation in which coordinates in two spaces are expressed rationally in terms of those in another.

Chain equivalences give an equivalence relation on the space of chain homomorphisms. Two chain complexes are chain equivalent if there are chain maps phi:C_*->D_* and ...

In mathematics, the term "collection" is generally used to mean a multiset, i.e., a set in which order is ignored but multiplicity is significant.

Let suma_k and sumb_k be a series with positive terms and suppose a_1<=b_1, a_2<=b_2, .... 1. If the bigger series converges, then the smaller series also converges. 2. If ...

While the above figure appears to be a sequence of nested squares, it actually consists of a single square spiral.

A curve has positive orientation if a region R is on the left when traveling around the outside of R, or on the right when traveling around the inside of R.

G = int_0^infty(e^(-u))/(1+u)du (1) = -eEi(-1) (2) = 0.596347362... (3) (OEIS A073003), where Ei(x) is the exponential integral. Stieltjes showed it has the continued ...