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The even part Ev(n) of a positive integer n is defined by Ev(n)=2^(b(n)), where b(n) is the exponent of the exact power of 2 dividing n. The values for n=1, 2, ..., are 1, 2, ...

The exponent laws, also called the laws of indices (Higgens 1998) or power rules (Derbyshire 2004, p. 65), are the rules governing the combination of exponents (powers). The ...

Fermat's sandwich theorem states that 26 is the only number sandwiched between a perfect square number (5^2=25) and a perfect cubic number (3^3=27). According to Singh ...

The nontrivial zeros of the Riemann zeta function correspond to the eigenvalues of some Hermitian operator (Derbyshire 2004, pp. 277-278).

Let S be a nonempty set of real numbers that has an upper bound. Then a number c is called the least upper bound (or the supremum, denoted supS) for S iff it satisfies the ...

A mathematical problem, usually not requiring advanced mathematics, to which a solution is desired. Puzzles frequently require the rearrangement of existing pieces (e.g., 15 ...

The term "real line" has a number of different meanings in mathematics. Most commonly, "real line" is used to mean real axis, i.e., a line with a fixed scale so that every ...

In logic, a term is a variable, constant, or the result of acting on variables and constants by function symbols. In algebra, a term is a product of the form x^n (in the ...

The three circles theorem, also called Hadamard's three circles theorem (Edwards 2001, p. 187), states that if f is an analytic function in the annulus 0<r_1<|z|<r_2<infty, ...

The tilde is the mark "~" placed on top of a symbol to indicate some special property. x^~ is voiced "x-tilde." The tilde symbol is commonly used to denote an operator. In ...