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Let E be an elliptic curve defined over the field of rationals Q(sqrt(-d)) having equation y^2=x^3+ax+b with a and b integers. Let P be a point on E with integer coordinates ...

A surface S is n-embeddable if it can be placed in R^n-space without self-intersections, but cannot be similarly placed in any R^k for k<n. A surface so embedded is said to ...

The center of an inner Soddy circle. It has equivalent triangle center functions alpha = 1+(2Delta)/(a(b+c-a)) (1) alpha = sec(1/2A)cos(1/2B)cos(1/2C)+1, (2) where Delta is ...

p is an equireciprocal point if, for every chord [x,y] of a curve C, p satisfies |x-p|^(-1)+|y-p|^(-1)=c for some constant c. The foci of an ellipse are equichordal points.

Erdős and Heilbronn (Erdős and Graham 1980) posed the problem of estimating from below the number of sums a+b where a in A and b in B range over given sets A,B subset= Z/pZ ...

The Diophantine equation sum_(j=1)^(m-1)j^n=m^n. Erdős conjectured that there is no solution to this equation other than the trivial solution 1^1+2^1=3^1, although this ...

The Erdős number is the number of "hops" needed to connect the author of a paper with the prolific late mathematician Paul Erdős. An author's Erdős number is 1 if he has ...

The sequence of numbers obtained by letting a_1=2, and defining a_n=lpf(1+product_(k=1)^(n-1)a_k) where lpf(n) is the least prime factor. The first few terms are 2, 3, 7, 43, ...

The Euler-Gergonne-Soddy triangle is the right triangle DeltaZFlEv created by the pairwise intersections of the Euler line L_E, Soddy line L_S, and Gergonne line L_G. (The ...

The numbers 2^npq and 2^nr are an amicable pair if the three integers p = 2^m(2^(n-m)+1)-1 (1) q = 2^n(2^(n-m)+1)-1 (2) r = 2^(n+m)(2^(n-m)+1)^2-1 (3) are all prime numbers ...