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If a and b are integers not both equal to 0, then there exist integers u and v such that GCD(a,b)=au+bv, where GCD(a,b) is the greatest common divisor of a and b.

Define a cell in R^1 as an open interval or a point. A cell in R^(k+1) then has one of two forms, {(x,y):x in C, and f(x)<y<g(x)} (1) or {(x,y):x in C, and y=f(x)}, (2) where ...

Experimental mathematics is a type of mathematical investigation in which computation is used to investigate mathematical structures and identify their fundamental properties ...

The extended greatest common divisor of two integers m and n can be defined as the greatest common divisor GCD(m,n) of m and n which also satisfies the constraint ...

The Frobenius equation is the Diophantine equation a_1x_1+a_2x_2+...+a_nx_n=b, where the a_i are positive integers, b is an integer, and the solutions x_i are nonnegative ...

An approach for the calculation of a Gröbner basis into several smaller computations following a path in the Gröbner fan of the ideal generated by the system of inequalities.

A linear combination of basis quaternions with integer coefficients.

The repeated application of a transformation.

Let F be a differential field with constant field K. For f in F, suppose that the equation g^'=f (i.e., g=intf) has a solution g in G, where G is an elementary extension of F ...

A method for constructing magic squares of odd order.