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Given the Mertens function defined by M(n)=sum_(k=1)^nmu(k), (1) where mu(n) is the Möbius function, Stieltjes claimed in an 1885 letter to Hermite that M(x)x^(-1/2) stays ...

A method used by Gauss to solve the quadratic Diophantine equation of the form mx^2+ny^2=A (Dickson 2005, pp. 391 and 407).

Model completion is a term employed when existential closure is successful. The formation of the complex numbers, and the move from affine to projective geometry, are ...

A shuffle in which cards from the top of the deck in the left hand are alternatively moved to the bottom and top of the deck in the right hand. If the deck is shuffled m ...

A nonempty finite set of n×n integer matrices for which there exists some product of the matrices in the set which is equal to the zero matrix.

Let S_N(s)=sum_(n=1)^infty[(n^(1/N))]^(-s), (1) where [x] denotes nearest integer function, i.e., the integer closest to x. For s>3, S_2(s) = 2zeta(s-1) (2) S_3(s) = ...

A function f(n) has the normal order F(n) if f(n) is approximately F(n) for almost all values of n. More precisely, if (1-epsilon)F(n)<f(n)<(1+epsilon)F(n) for every positive ...

g_(ij)=[0 1 0 0; 1 0 0 0; 0 0 0 -1; 0 0 -1 0]. It can be expressed as g_(ab)=l_an_b+l_bn_a-m_am^__b-m_bm^__a.

The study of numbers for the supposed purpose of predicting future events or seeking connections with the occult.

An expression that is of a given type. For example, all primes p>3 are "of the form" 6n+/-1. The term "of shape" is sometimes also used.