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If there is an integer 0<x<p such that x^2=q (mod p), (1) i.e., the congruence (1) has a solution, then q is said to be a quadratic residue (mod p). Note that the trivial ...

Every semisimple Lie algebra g is classified by its Dynkin diagram. A Dynkin diagram is a graph with a few different kinds of possible edges. The connected components of the ...

The series of Sturm functions arising in application of the Sturm theorem.

The arithmetic mean of a set of values is the quantity commonly called "the" mean or the average. Given a set of samples {x_i}, the arithmetic mean is x^_=1/Nsum_(i=1)^Nx_i. ...

The graph distance matrix, sometimes also called the all-pairs shortest path matrix, is the square matrix (d_(ij)) consisting of all graph distances from vertex v_i to vertex ...

Three circles packed inside a triangle such that each is tangent to the other two and to two sides of the triangle are known as Malfatti circles. The Malfatti configuration ...

The regular heptagon is the seven-sided regular polygon illustrated above, which has Schläfli symbol {7}. According to Bankoff and Garfunkel (1973), "since the earliest days ...

The q-analog of the Pochhammer symbol defined by (a;q)_k={product_(j=0)^(k-1)(1-aq^j) if k>0; 1 if k=0; product_(j=1)^(|k|)(1-aq^(-j))^(-1) if k<0; ...

A problem listed in a fall issue of Gazeta Matematică in the mid-1970s posed the question if x_1>0 and x_(n+1)=(1+1/(x_n))^n (1) for n=1, 2, ..., then are there any values ...

A method for finding roots of a polynomial equation f(x)=0. Now find an equation whose roots are the roots of this equation diminished by r, so (1) The expressions for f(r), ...