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The base of a number system, i.e., 2 for binary, 8 for octal, 10 for decimal, and 16 for hexadecimal. The radix is sometimes called the base or scale.

If f is continuous on a closed interval [a,b], and c is any number between f(a) and f(b) inclusive, then there is at least one number x in the closed interval such that ...

The logarithm log_bx for a base b and a number x is defined to be the inverse function of taking b to the power x, i.e., b^x. Therefore, for any x and b, x=log_b(b^x), (1) or ...

A Proth number that is prime, i.e., a number of the form N=k·2^n+1 for odd k, n a positive integer, and 2^n>k. Factors of Fermat numbers are of this form as long as they ...

The (unilateral) Z-transform of a sequence {a_k}_(k=0)^infty is defined as Z[{a_k}_(k=0)^infty](z)=sum_(k=0)^infty(a_k)/(z^k). (1) This definition is implemented in the ...

The (unilateral) Z-transform of a sequence {a_k}_(k=0)^infty is defined as Z[{a_k}_(k=0)^infty](z)=sum_(k=0)^infty(a_k)/(z^k). (1) This definition is implemented in the ...

Let A be the area of a simply closed lattice polygon. Let B denote the number of lattice points on the polygon edges and I the number of points in the interior of the ...

The Dirichlet kernel D_n^M is obtained by integrating the number theoretic character e^(i<xi,x>) over the ball |xi|<=M, D_n^M=-1/(2pir)d/(dr)D_(n-2)^M.

The only whole number solution to the Diophantine equation y^3=x^2+2 is y=3, x=+/-5. This theorem was offered as a problem by Fermat, who suppressed his own proof.

For a real number x, the mantissa is defined as the positive fractional part x-|_x_|=frac(x), where |_x_| denotes the floor function. For example, for x=3.14159, the mantissa ...