Search Results for ""

A sequence {x_1,x_2,...} is equidistributed iff lim_(N->infty)1/Nsum_(n<N)e^(2piimx_n)=0 for each m=1, 2, .... A consequence of this result is that the sequence {frac(nx)} is ...

The absolute difference of two numbers n_1 and n_2 is |n_1-n_2|, where the minus sign denotes subtraction and |x| denotes the absolute value.

A pair of consecutive numbers.

The probability that a random integer between 1 and x will have its greatest prime factor <=x^alpha approaches a limiting value F(alpha) as x->infty, where F(alpha)=1 for ...

The difference of two numbers n_1 and n_2 is n_1-n_2, where the minus sign denotes subtraction.

A set of m distinct positive integers S={a_1,...,a_m} satisfies the Diophantus property D(n) of order n (a positive integer) if, for all i,j=1, ..., m with i!=j, ...

The ancient Greeks used the 24 letters of their alphabet plus three special signs called episemons--vau or digamma or stigma (6), koppa or qoppa (90), and san or sampi ...

The rules for the multiplication of quaternions.

One of the most useful tools in nonstandard analysis is the concept of a hyperfinite set. To understand a hyperfinite set, begin with an arbitrary infinite set X whose ...

A conjecture concerning primes.