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The j-function is the modular function defined by j(tau)=1728J(tau), (1) where tau is the half-period ratio, I[tau]>0, ...

The fraction of odd values of the partition function P(n) is roughly 50%, independent of n, whereas odd values of Q(n) occur with ever decreasing frequency as n becomes ...

Bertrand's postulate, also called the Bertrand-Chebyshev theorem or Chebyshev's theorem, states that if n>3, there is always at least one prime p between n and 2n-2. ...

As a consequence of Matiyasevich's refutation of Hilbert's 10th problem, it can be proved that there does not exist a general algorithm for solving a general quartic ...

The function lambda(n)=(-1)^(Omega(n)), (1) where Omega(n) is the number of not necessarily distinct prime factors of n, with Omega(1)=0. The values of lambda(n) for n=1, 2, ...

The 2-1 equation A^n+B^n=C^n (1) is a special case of Fermat's last theorem and so has no solutions for n>=3. Lander et al. (1967) give a table showing the smallest n for ...

A prime factor is a factor that is prime, i.e., one that cannot itself be factored. In general, a prime factorization takes the form ...

As a part of the study of Waring's problem, it is known that every positive integer is a sum of no more than 9 positive cubes (g(3)=9), that every "sufficiently large" ...

Let (x_1,x_2) and (y_1,y_2,y_3) be two sets of complex numbers linearly independent over the rationals. Then at least one of ...

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, ...