Search Results for ""

Let a_n>=0 and suppose sum_(n=1)^inftya_ne^(-an)∼1/a as a->0^+. Then sum_(n<=x)a_n∼x as x->infty. This theorem is a step in the proof of the prime number theorem, but has ...

Let Gamma be an algebraic curve in a projective space of dimension n, and let p be the prime ideal defining Gamma, and let chi(p,m) be the number of linearly independent ...

If the period of a repeating decimal for a/p, where p is prime and a/p is a reduced fraction, has an even number of digits, then dividing the repeating portion into halves ...

An integer which is expressible in only one way in the form x^2+Dy^2 or x^2-Dy^2 where x^2 is relatively prime to Dy^2. If the integer is expressible in more than one way, it ...

An integer which is expressible in more than one way in the form x^2+Dy^2 or x^2-Dy^2 where x^2 is relatively prime to Dy^2. If the integer is expressible in only one way, it ...

An irreducible algebraic integer which has the property that, if it divides the product of two algebraic integers, then it divides at least one of the factors. 1 and -1 are ...

A proposition is a mathematical statement such as "3 is greater than 4," "an infinite set exists," or "7 is prime." An axiom is a proposition that is assumed to be true. With ...

Hoffman (1998, p. 90) calls the sum of the exponents in the prime factorization of a number its roundness. The first few values for n=1, 2, ... are 0, 1, 1, 2, 1, 2, 1, 3, 2, ...

If the integral coefficients C_0, C_1, ..., C_(N-1) of the polynomial f(x)=C_0+C_1x+C_2x^2+...+C_(N-1)x^(N-1)+x^N are divisible by a prime number p, while the free term C_0 ...

sum_(n=1)^(infty)1/(phi(n)sigma_1(n)) = product_(p prime)(1+sum_(k=1)^(infty)1/(p^(2k)-p^(k-1))) (1) = 1.786576459... (2) (OEIS A093827), where phi(n) is the totient function ...