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A system of congruences a_i mod n_i with 1<=i<=k is called a complete residue system (or covering system) if every integer y satisfies y=a_i (mod n) for at least one value of ...

The Jacobi symbol (a/y)=chi(y) as a number theoretic character can be extended to the Kronecker symbol (f(a)/y)=chi^*(y) so that chi^*(y)=chi(y) whenever chi(y)!=0. When y is ...

The eight of Hilbert's axioms which concern collinearity and intersection; they include the first four of Euclid's postulates.

Isomorphism is a very general concept that appears in several areas of mathematics. The word derives from the Greek iso, meaning "equal," and morphosis, meaning "to form" or ...

Let t(m) denote the set of the phi(m) numbers less than and relatively prime to m, where phi(n) is the totient function. Then if S_m=sum_(t(m))1/t, (1) then {S_m=0 (mod m^2) ...

In space, the only conformal mappings are inversions, similarity transformations, and congruence transformations. Or, restated, every angle-preserving transformation is a ...

The minimal residue of a (mod m) is the value b or b-m, whichever is smaller in absolute value, where a=b (mod m). If m=2b (so that b=|b-m|), then the minimal residue is ...

The four of Hilbert's axioms which concern the arrangement of points.

In general, a remainder is a quantity "left over" after performing a particular algorithm. The term is most commonly used to refer to the number left over when two integers ...

Specifying two sides and the angle between them uniquely (up to geometric congruence) determines a triangle. Let c be the base length and h be the height. Then the area is ...