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Mills (1947) proved the existence of a real constant A such that |_A^(3^n)_| (1) is prime for all integers n>=1, where |_x_| is the floor function. Mills (1947) did not, ...

Half-angle formulas and formulas expressing trigonometric functions of an angle x/2 in terms of functions of an angle x. For real x, sin(1/2x) = ...

Hardy and Littlewood (1914) proved that the sequence {frac(x^n)}, where frac(x) is the fractional part, is equidistributed for almost all real numbers x>1 (i.e., the ...

Long multiplication is the method of multiplication that is commonly taught to elementary school students throughout the world. It can be used on two numbers of arbitrarily ...

A Dirichlet L-series is a series of the form L_k(s,chi)=sum_(n=1)^inftychi_k(n)n^(-s), (1) where the number theoretic character chi_k(n) is an integer function with period k, ...

Any set which can be put in a one-to-one correspondence with the natural numbers (or integers) so that a prescription can be given for identifying its members one at a time ...

A generalized continued fraction is an expression of the form b_0+(a_1)/(b_1+(a_2)/(b_2+(a_3)/(b_3+...))), (1) where the partial numerators a_1,a_2,... and partial ...

In the fields of functional and harmonic analysis, the Littlewood-Paley decomposition is a particular way of decomposing the phase plane which takes a single function and ...

An algorithm which can be used to find integer relations between real numbers x_1, ..., x_n such that a_1x_1+a_2x_2+...+a_nx_n=0, with not all a_i=0. Although the algorithm ...

The angles mpi/n (with m,n integers) for which the trigonometric functions may be expressed in terms of finite root extraction of real numbers are limited to values of m ...