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Find a square number x^2 such that, when a given integer h is added or subtracted, new square numbers are obtained so that x^2+h=a^2 (1) and x^2-h=b^2. (2) This problem was ...

A rooted graph is a graph in which one node is labeled in a special way so as to distinguish it from other nodes. The special node is called the root of the graph. The rooted ...

A double bubble is pair of bubbles which intersect and are separated by a membrane bounded by the intersection. The usual double bubble is illustrated in the left figure ...

In a given triangle DeltaABC with all angles less than 120 degrees (2pi/3, the first Fermat point X or F_1 (sometimes simply called "the Fermat point," Torricelli point, or ...

The term "square" can be used to mean either a square number ("x^2 is the square of x") or a geometric figure consisting of a convex quadrilateral with sides of equal length ...

A grouping of statistics.

There are two different definitions of generalized Fermat numbers, one of which is more general than the other. Ribenboim (1996, pp. 89 and 359-360) defines a generalized ...

A group that has a primitive group action.

A specific prescription for carrying out a task or solving a problem. Also called an algorithm, method, or technique

If there is no integer 0<x<p such that x^2=q (mod p), i.e., if the congruence (35) has no solution, then q is said to be a quadratic nonresidue (mod p). If the congruence ...