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The term perfect square is used to refer to a square number, a perfect square dissection, or a factorable quadratic polynomial of the form a^2+/-2ab+b^2=(a+/-b)^2.

A sequence {a_i} is said to be periodic with period p with if it satisfies a_i=a_(i+np) for n=1, 2, .... For example, {1,2,1,2,1,2,1,2,1,2,1,2,1,2,...} is a periodic sequence ...

The knot move obtained by fixing disk 1 in the figure above and flipping disks 2 and 3.

The use of permil (a.k.a. parts per thousand) is a way of expressing ratios in terms of whole numbers. Given a ratio or fraction, it is converted to a permil-age by ...

int_0^z(t^mu)/(1+t)dt=z/(mu+1+((mu+1)^2z)/((mu+2)-(mu+1)z+((mu+2)^2z)/((mu+3)-(mu+2)z+...))) for mu>-1 and -1<z<=1 (Perron 1954-1957, p. 18; Borwein et al. 2004, p. 35).

An analog of the determinant for number triangles defined as a signed sum indexed by set partitions of {1,...,n} into pairs of elements. The Pfaffian is the square root of ...

The addition of two quantities, i.e., a plus b. The operation is denoted a+b, and the symbol + is called the plus sign. Floating-point addition is sometimes denoted direct ...

Let p be an odd prime, k be an integer such that pk and 1<=k<=2(p+1), and N=2kp+1. Then the following are equivalent 1. N is prime. 2. There exists an a such that ...

Let n-1=FR where F is the factored part of a number F=p_1^(a_1)...p_r^(a_r), (1) where (R,F)=1, and R<sqrt(n). Pocklington's theorem, also known as the Pocklington-Lehmer ...

f(z)=k/((cz+d)^r)f((az+b)/(cz+d)) where I[z]>0.