Integer

Common short integer sizes Long integer A long integer can represent a whole integer whose range is greater than or equal to that of a standard integer on the same machine.

All Gaussian integers on such a line are integer multiples of some Gaussian integer h. But then the integer gh ≠ ±1 divides both a and b.) Second, it follows that z and z* likewise share no prime factors in the Gaussian integers.

Integer unknowns If all of the unknown variables are required to be integers, then the problem is called an integer programming (IP) or integer linear programming (ILP) problem.

Number theory Diophantine equations main A Diophantine equation is a polynomial equation in two or more unknowns for which only the integer solutions are sought (an integer solution is a solution such that all the unknowns take integer values).

The notation E : t can be read as expression E has type t. For instance, the argument n is assigned type integer (int), and fac (n : int), the result of applying fac to the integer n, also has type integer.

This is a paradox: there must be an integer defined by this expression, but since the expression is self-contradictory (any integer it defines is definable in under sixty letters), there cannot be any integer defined by it.

Thus the 32-bit integer Integer and 32-bit floating-point Float objects can simply use the value directly; whereas the 64-bit integer Long and 64-bit floating-point Double cannot use this method.

It’s hard to remember that many names, so each player wears a jersey with a unique positive integer on the back (so that there is a player for every integer).

According to Professor Gilles Brassard, an expert in quantum computing: "The time needed to factor an RSA integer is the same order as the time needed to use that same integer as modulus for a single RSA encryption.

A CPU's integer size determines the range of integer values it can directly operate on.

All multiples are integer powers of ten, and above a hundred or below a hundredth all are integer powers of a thousand.

A method of constructing a magic square of doubly even order Doubly even means that n is an even multiple of an even integer; or 4p (e.g. 4, 8, 12), where p is an integer.

An example is the " divides " relation between the set of prime numbers P and the set of integers Z, in which every prime p is associated with every integer z that is a multiple of p (but with no integer that is not a multiple of p).

Any integer with absolute value less than 2 24 can be exactly represented in the single precision format, and any integer with absolute value less than 2 53 can be exactly represented in the double precision format.

Apart from division by zero being undefined, the quotient is not an integer unless the dividend is an integer multiple of the divisor.

A standing wave like this can have 0,1,2, or any integer number of wavelengths around the circle, but it cannot have a non-integer number of wavelengths like 8.3.

As with single-precision floating-point format, it lacks precision on integer numbers when compared with an integer format of the same size.

Complete sequences An integer sequence is called a complete sequence if every positive integer can be expressed as a sum of values in the sequence, using each value at most once.

Consequently, the inverse of an integer matrix is an integer matrix if and only if the determinant is 1 or -1. ).

Conversely, (4) shows that any integer-valued polynomial is an integer linear combination of these binomial coefficient polynomials.