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Elementary number theory is the branch of number theory in which elementary methods (i.e., arithmetic, geometry, and high school algebra) are used to solve equations with ...

The identity PVint_(-infty)^inftyF(phi(x))dx=PVint_(-infty)^inftyF(x)dx (1) holds for any integrable function F(x) and phi(x) of the form ...

A multinomial series is generalization of the binomial series discovered by Johann Bernoulli and Leibniz. The multinomial series arises in a generalization of the binomial ...

The series which arises in the binomial theorem for negative integer -n, (x+a)^(-n) = sum_(k=0)^(infty)(-n; k)x^ka^(-n-k) (1) = sum_(k=0)^(infty)(-1)^k(n+k-1; k)x^ka^(-n-k) ...

A number theoretic function is a function whose domain is the set of positive integers.

The number of digits used to perform a given computation. The concepts of accuracy and precision are both closely related and often confused. While the accuracy of a number x ...

A metric space Z^^ in which the closure of a congruence class B(j,m) is the corresponding congruence class {x in Z^^|x=j (mod m)}.

A word derived from the Latin roots quad- (four) and via (ways, roads), therefore a crossing of four roads. In medieval universities, the quadrivium consisted of the four ...

If f(x)=f_0+f_1x+f_2x^2+...+f_nx^n+..., (1) then S(n,j)=f_jx^j+f_(j+n)x^(j+n)+f_(j+2n)x^(j+2n)+... (2) is given by S(n,j)=1/nsum_(t=0)^(n-1)w^(-jt)f(w^tx), (3) where ...

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 ...