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The least common multiple of two numbers a and b, variously denoted LCM(a,b) (this work; Zwillinger 1996, p. 91; Råde and Westergren 2004, p. 54), lcm(a,b) (Gellert et al. ...

A rigorous mathematical argument which unequivocally demonstrates the truth of a given proposition. A mathematical statement that has been proven is called a theorem. ...

The prime counting function is the function pi(x) giving the number of primes less than or equal to a given number x (Shanks 1993, p. 15). For example, there are no primes ...

Construct a square equal in area to a circle using only a straightedge and compass. This was one of the three geometric problems of antiquity, and was perhaps first attempted ...

The figure determined by four lines, no three of which are concurrent, and their six points of intersection (Johnson 1929, pp. 61-62). Note that this figure is different from ...

Let the divisor function d(n) be the number of divisors of n (including n itself). For a prime p, d(p)=2. In general, sum_(k=1)^nd(k)=nlnn+(2gamma-1)n+O(n^theta), where gamma ...

The Eisenstein integers, sometimes also called the Eisenstein-Jacobi integers (Finch 2003, p. 601), are numbers of the form a+bomega, where a and b are normal integers, ...

Let the elliptic modulus k satisfy 0<k^2<1, and the Jacobi amplitude be given by phi=amu with -pi/2<phi<pi/2. The incomplete elliptic integral of the first kind is then ...

Gaussian elimination is a method for solving matrix equations of the form Ax=b. (1) To perform Gaussian elimination starting with the system of equations [a_(11) a_(12) ... ...

A Gaussian integer is a complex number a+bi where a and b are integers. The Gaussian integers are members of the imaginary quadratic field Q(sqrt(-1)) and form a ring often ...