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A symmetric matrix is a square matrix that satisfies A^(T)=A, (1) where A^(T) denotes the transpose, so a_(ij)=a_(ji). This also implies A^(-1)A^(T)=I, (2) where I is the ...

The number of colors sufficient for map coloring on a surface of genus g is given by the Heawood conjecture, chi(g)=|_1/2(7+sqrt(48g+1))_|, where |_x_| is the floor function. ...

A divisor d of n for which GCD(d,n/d)=1, (1) where GCD(m,n) is the greatest common divisor. For example, the divisors of 12 are {1,2,3,4,6,12}, so the unitary divisors are ...

A vector space V is a set that is closed under finite vector addition and scalar multiplication. The basic example is n-dimensional Euclidean space R^n, where every element ...

The Weierstrass zeta function zeta(z;g_2,g_3) is the quasiperiodic function defined by (dzeta(z;g_2,g_3))/(dz)=-P(z;g_2,g_3), (1) where P(z;g_2,g_3) is the Weierstrass ...

Wolfram (2002, p. 123) considered the sequence related to the Collatz problem obtained by iterating w_n={3/2w_(n-1) for w_(n-1) even; 3/2(w_(n-1)+1) for w_(n-1) odd (1) ...

Let {f_n} and {a_n} be sequences with f_n>=f_(n+1)>0 for n=1, 2, ..., then |sum_(n=1)^ma_nf_n|<=Af_1, where A=max{|a_1|,|a_1+a_2|,...,|a_1+a_2+...+a_m|}.

The absolute difference of two numbers n_1 and n_2 is |n_1-n_2|, where the minus sign denotes subtraction and |x| denotes the absolute value.

An additive function is an arithmetic function such that whenever positive integers a and b are relatively prime, f(ab)=f(a)+f(b). An example of an additive function is ...

A mathematical object S is said to be additively closed if a,b in S implies that a+b in S.