The principal quantum number, n, describes the energy of the electron and is always a positive integer.

The azimuthal quantum number,, describes the orbital angular momentum of each electron and is a non-negative integer.

The magnetic quantum number,, describes the magnetic moment of an electron in an arbitrary direction, and is also always an integer.

The quantum Hall effect was discovered by Klaus von Klitzing in 1980 when he observed the Hall conductivity to be integer multiples of a fundamental constant.

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.

The spin-statistics theorem holds that, in any reasonable relativistic quantum field theory, particles with integer spin are bosons, while particles with half-integer spin are fermions.

In contrast, particles with integer spin ( called bosons ) have symmetric wave functions ; unlike fermions they may share the same quantum states.

According to the spin-statistics theorem, particles with integer spin occupy symmetric quantum states, and particles with half-integer spin occupy antisymmetric states ; furthermore, only integer or half-integer values of spin are allowed by the principles of quantum mechanics.

Large-scale quantum computers could be able to solve certain problems much faster than any classical computer by using the best currently known algorithms, like integer factorization using Shor's algorithm or the simulation of quantum many-body systems.

This ability would allow a quantum computer to decrypt many of the cryptographic systems in use today, in the sense that there would be a polynomial time ( in the number of digits of the integer ) algorithm for solving the problem.

If one used Planck's energy quanta, and demanded that electromagnetic radiation at a given frequency could only transfer energy to matter in integer multiples of an energy quantum hν, then the photoelectric effect could be explained very simply.

Shor's algorithm, named after mathematician Peter Shor, is a quantum algorithm ( an algorithm which runs on a quantum computer ) for integer factorization formulated in 1994.

On a quantum computer, to factor an integer N, Shor's algorithm runs in polynomial time ( the time taken is polynomial in log N, which is the size of the input ).

Specifically it takes time, demonstrating that the integer factorization problem can be efficiently solved on a quantum computer and is thus in the complexity class BQP.

The quantum Hall effect ( or integer quantum Hall effect ) is a quantum-mechanical version of the Hall effect, observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall conductivity σ takes on the quantized values

The quantum Hall effect is referred to as the integer or fractional quantum Hall effect depending on whether ν is an integer or fraction respectively.

The integer quantum Hall effect is very well understood, and can be simply explained in terms of single-particle orbitals of an electron in a magnetic field ( see Landau quantization ).

It is also very well understood as an integer quantum Hall effect, not of electrons but of charge-flux composites known as composite fermions.

Actual measurements of the Hall conductance have been found to be integer or fractional multiples of e < sup > 2 </ sup >/ h to nearly one part in a billion.

The integer quantization of the Hall conductance was originally predicted by Ando, Matsumoto, and Uemura in 1975, on the basis of an approximate calculation which they themselves did not believe to be true.

Most integer quantum Hall experiments are now performed on gallium arsenide heterostructures, although many other semiconductor materials can be used.

In 2007, the integer quantum Hall effect was reported in graphene at temperatures as high as room temperature, and in the oxide ZnO-Mg < sub > x </ sub > Zn < sub > 1-x </ sub > O.

The colors represent the integer Hall conductances.

The observed strong similarity between integer and fractional quantum Hall effects is explained by the tendency of electrons to form bound states with an even number of magnetic flux quanta, called composite fermions.

Klaus von Klitzing ( 28 June 1943 in Schroda ) is a German physicist known for discovery of the integer quantum Hall Effect, for which he was awarded the 1985 Nobel Prize in Physics.

This level is responsible for the anomalous integer quantum Hall effect.

A Hall divisor of an integer n is a divisor d of n such that

In effect, integer size sets a hardware limit on the range of integers the software run by the CPU can utilize.

( see figure ) The effect was observed to be independent of parameters such as the system size and impurities, and in 1981, theorist Robert Laughlin proposed a theory describing the integer states in terms of a topological invariant called the Chern number.

The effect of the prefixes is to multiply or divide the unit by a factor of ten, one hundred or an integer power of one thousand.

There are an infinite number of irrational reciprocal pairs that differ by an integer ( giving the curious effect that the pairs share their infinite mantissa ).

This has the effect of keeping the middle bits ; the < var > I </ var >- number of least significant integer bits, and the < var > Q </ var >- number of most significant fractional bits.

The Dirac string acts as the solenoid in the Aharonov-Bohm effect, and the requirement that the position of the Dirac string should not be observable implies the Dirac quantization rule: the product of a magnetic charge and an electric charge must always be an integer multiple of.

For integer order α = n, J < sub > n </ sub > is often defined via a Laurent series for a generating function:

This can be proved ( for integer t ) by using the formula for geometric series: ( using y = 1-x )

In mathematics, the Fibonacci numbers or Fibonacci series or Fibonacci sequence are the numbers in the following integer sequence:

Leonhard Euler considered the above series in 1740 for positive integer values of s, and later Chebyshev extended the definition to real s > 1.

In systems without any floating-point hardware, the CPU emulates it using a series of simpler fixed-point arithmetic operations that run on the integer arithmetic logic unit.

A time series taken for one time-difference τ < sub > 0 </ sub > can be used to generate Allan variance for any τ being an integer multiple of τ < sub > 0 </ sub > in which case τ = nτ < sub > 0 </ sub > is being used, and n becomes a variable for the estimator.

For most string instruments and other long and thin instruments such as a trombone or bassoon, the first few overtones are quite close to integer multiples of the fundamental frequency, producing an approximation to a harmonic series.

The familiar decimal notation for real numbers can also be viewed as an example of a power series, with integer coefficients, but with the argument x fixed at.

For a non-zero formal Laurent series, the minimal integer n such that a < sub > n </ sub >≠ 0 is called the order of f, denoted ord ( f ).

When n is an integer, the solution P < sub > n </ sub >( x ) that is regular at x = 1 is also regular at x = − 1, and the series for this solution terminates ( i. e. is a polynomial ).

The fact that it is almost exactly 19, 756 days ( a whole integer ) ensures each successive eclipse in the series occurs very close to the previous eclipse in the series.

* Evaluation of infinite series, infinite products and integrals ( also see symbolic integration ), typically by carrying out a high precision numerical calculation, and then using an integer relation algorithm ( such as the Inverse Symbolic Calculator ) to find a linear combination of mathematical constants that matches this value.

If A has a composition series, the integer n only depends on A and is called the length of A.

Ideally, the overtone series of a note consists of frequencies that are integer multiples of the note's fundamental frequency.

Initially e is assumed to be a rational number of the form a / b. We then analyze a blown-up difference x of the series representing e and its strictly smaller partial sum, which approximates the limiting value e. By choosing the magnifying factor to be the factorial of b, the fraction a / b and the partial sum are turned into integers, hence x must be a positive integer.

* If any b < sub > k </ sub > is a non-positive integer ( excepting the previous case with − b < sub > k </ sub > < a < sub > j </ sub >) then the denominators become 0 and the series is undefined.

provided that m is a non-negative integer ( so that the series terminates ) and

For each positive integer N ≥ 1, let S < sub > N </ sub > f be the Nth partial Fourier series

The Lucas numbers or Lucas series are an integer sequence named after the mathematician François Édouard Anatole Lucas ( 1842 – 1891 ), who studied both that sequence and the closely related Fibonacci numbers.

A divisive ( or, more commonly, multiplicative ) rhythm is a rhythm in which a larger period of time is divided into smaller rhythmic units or, conversely, some integer unit is regularly multiplied into larger, equal units ; this can be contrasted with additive rhythm, in which larger periods of time are constructed by concatenating ( joining end to end ) a series of units into larger units of unequal length, such as a 5 / 8 meter produced by the regular alternation of 2 / 8 and 3 / 8 ( London 2001, § I. 8 ).

Then f is either zero, or the first nonzero term in its power series expansion is for some non-negative integer h, called the height of the homomorphism f. The height of the zero homomorphism is defined to be ∞.

The product for any larger non-zero integer can be found by a series of additions to each of its digits from right to left, two at a time.

The proof is by the method of discrete Taylor series: binomial coefficients are integer-valued polynomials, and conversely, the discrete difference of an integer series is an integer series, so the discrete Taylor series of an integer series generated by a polynomial has integer coefficients ( and is a finite series ).