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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 ...

A theorem which asserts that if a sequence or function behaves regularly, then some average of it behaves regularly. For example, A(x)∼x implies A_1(x)=int_0^xA(t)dt∼1/2x^2 ...

If an aliquot sequence {s^0(n),s(n),s^2(n),...} for a given n is bounded, it either ends at s(1)=0 or becomes periodic. If the sequence is periodic (or eventually periodic), ...

Two points are antipodal (i.e., each is the antipode of the other) if they are diametrically opposite. Examples include endpoints of a line segment, or poles of a sphere. ...

The set C_(n,m,d) of all m-D varieties of degree d in an n-dimensional projective space P^n into an M-D projective space P^M.

A complex translation is a map of the form z|->z+a, where a is a fixed complex number, which corresponds to translation (shifting) of points the complex plane by the complex ...

The real projective plane with elliptic metric where the distance between two points P and Q is defined as the radian angle between the projection of the points on the ...

A continuum that is not decomposable is an indecomposable continuum.

For a group G, consider a subgroup H with elements h_i and an element x of G not in H, then xh_i for i=1, 2, ... constitute the left coset of the subgroup H with respect to x.

Let n be a positive number having primitive roots. If g is a primitive root of n, then the numbers 1, g, g^2, ..., g^(phi(n)-1) form a reduced residue system modulo n, where ...