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A multiple of a number x is any quantity y=nx with n an integer. If x and y are integers, then x is called a factor of y. The smallest positive number m for which there exist ...

The parity of an integer is its attribute of being even or odd. Thus, it can be said that 6 and 14 have the same parity (since both are even), whereas 7 and 12 have opposite ...

The Klein-Beltrami model of hyperbolic geometry consists of an open disk in the Euclidean plane whose open chords correspond to hyperbolic lines. Two lines l and m are then ...

Two submanifolds X and Y in an ambient space M intersect transversally if, for all p in X intersection Y, TX_p+TY_p={v+w:v in TX_p,w in TY_p}=TM_p, where the addition is in ...

The genus gamma(G) of a graph G is the minimum number of handles that must be added to the plane to embed the graph without any crossings. A graph with genus 0 is embeddable ...

A test which always identifies prime numbers correctly, but may incorrectly identify a composite number as a prime.

One of the Plücker characteristics, defined by p=1/2(n-1)(n-2)-(delta+kappa)=1/2(m-1)(m-2)-(tau+iota), where m is the class, n the order, delta the number of nodes, kappa the ...

The first quadratic nonresidue mod p of a number is always less than 3(lnp)^2/2 (Wedeniwski 2001).

The identity F_n^4-F_(n-2)F_(n-1)F_(n+1)F_(n+2)=1, where F_n is a Fibonacci number.

If a real algebraic curve has no singularities except nodes and cusps, bitangents, and inflection points, then n+2tau_2^'+iota^'=m+2delta_2^'+kappa^', where n is the order, ...