If A and B are distinguishable particles, then the composite system has four distinct states:,,, and.

If A and B are identical bosons, then the composite system has only three distinct states:,, and.

If A and B are identical fermions, there is only one state available to the composite system: the totally antisymmetric state.

If the first system is in state and the second in state, the state of the composite system is

If one uses a composite representation of an " overall " reaction, some may be rational fractions.

Fermat's little theorem states that if p is prime and a is coprime to p, then a < sup > p − 1 </ sup > − 1 is divisible by p. If a composite integer x is coprime to an integer a > 1 and x divides a < sup > x − 1 </ sup > − 1, then x is called a Fermat pseudoprime to base a.

If a material with high strength in tension, such as steel, is placed in concrete, then the composite material, reinforced concrete, resists not only compression but also bending and other direct tensile actions.

If the Euler criterion formula is used modulo a composite number, the result may or may not be the value of the Jacobi symbol.

Fermat's test for compositeness, which is based on Fermat's little theorem, works as follows: given an integer n, choose some integer a coprime to n and calculate a < sup > n − 1 </ sup > modulo n. If the result is different from 1, n is composite.

The idea is that while there are composite probable primes to base a for any fixed a, we may hope there exists some fixed P < 1 such that for any given composite n, if we choose a randomly the probability that n is pseudoprime to base a is at most P. If we repeat this test k times, choosing a new a each time, the probability of n being pseudoprime to all the as tested is hence at most P < sup > k </ sup >, and as this decreases exponentially, only moderate k is required to make this probability negligibly small ( compared to, for example, the probability of computer hardware error ).

If programmers find that they are using multiple objects in the same way, and often have nearly identical code to handle each of them, then composite is a good choice ; it is less complex in this situation to treat primitives and composites as homogeneous.

check whether any integer m from 2 to n / 2 divides n. If n is divisible by any m then n is composite, otherwise it is prime.

If it is divisible by any of those numbers then it is composite, and any further tests can be skipped.

# Check some equality ( corresponding to the chosen test ) involving a and the given number n. If the equality fails to hold true, then n is a composite number, a is known as a witness for the compositeness, and the test stops.

: Given an integer n, choose some integer a coprime to n and calculate a < sup > n − 1 </ sup > modulo n. If the result is different from 1, then n is composite.

The solution is to make the test probabilistic: we choose nonzero randomly, and check whether or not it is a witness for the compositeness of n. If n is composite, most of the choices for a will be witnesses, and the test will detect n as composite with high probability.

If n is composite then the Miller – Rabin primality test declares n probably prime with a probability at most 4 < sup >− k </ sup >.

If the tested number n is composite, the strong liars a coprime to n are contained in a proper subgroup of the group, which means that if we test all a from a set which generates, one of them must be a witness for the compositeness of n. Assuming the truth of the generalized Riemann hypothesis ( GRH ), it is known that the group is generated by its elements smaller than O (( log n )< sup > 2 </ sup >), which was already noted by Miller.

There is a generalization of the Legendre symbol for composite values of p, the Jacobi symbol, but its properties are not as simple: if m is composite and the Jacobi symbol then a N m, and if a R m then but if we do not know whether a R m or a N m. If m is prime, the Jacobi and Legendre symbols agree.

If these particles were to collide and stick, the mass of the composite object would be 10 GeV / c < sup > 2 </ sup >.

If n is composite it is divisible by some prime number q, where.

If we cannot stop warfare in our own economic system, how can we expect to abolish it internationally??

If your house is to have a forced warm air system, cooling can be a part of it.

If you plan to add cooling later to your heating system, there are things to watch for.

If the problems of combining cooling with your heating are knotty, it may be cheaper to plan on a completely separate cooling system.

If you use one of the new year-round cooling system fluids such as `` Dowguard '' be sure to check it.

If Af is the change per unit volume in Gibbs function caused by the shear field at constant P and T, and **yr is the density of the fluid, then the total potential energy of the system above the reference height is Af.

If tyrosine and a system generating hydrogen peroxide are added to a cell-free homogenate of the thyroid, large quantities of free mono-iodotyrosine can be formed ( Alexander, 1959 ).

If the house is not wired adequately for electricity or if plumbing or a central heating system must be installed, check into the cost of making these improvements.

If laborers are merely commodities competing against each other in a market place like so many bags of wheat and corn ( unsupported, by the way, by any agricultural subsidy ), then they may be pardoned for reacting with complete antagonism to a system that imposes such status upon them.

If the demands of these two sovereigns upon his duty of allegiance come into conflict, those of the United States have the paramount authority in American law ; likewise, those of the foreign land have paramount authority in their legal system.

If we use a cylindrical coordinate system with basis vectors, then the gradient of and the divergence of are given by

If under the existing system he could not assemble forces quickly enough to intercept mobile Viking raiders, the obvious answer was to have a standing field force.

If administrative appeal is available, no appeal to the judicial system may be made.

If the system be entirely behind the aperture stop, then this is itself the entrance pupil ( front stop ); if entirely in front, it is the exit pupil ( back stop ).

If the object point be infinitely distant, all rays received by the first member of the system are parallel, and their intersections, after traversing the system, vary according to their perpendicular height of incidence, i. e. their distance from the axis.

If a system consists of several particles, the total angular momentum about a point can be obtained by adding ( or integrating ) all the angular momenta of the constituent particles.

If not, the system may either be rejected or accepted on conditions previously agreed between the sponsor and the manufacturer.

If the pressure in a system remains constant ( isobaric ), a vapor at saturation temperature will begin to condense into its liquid phase as thermal energy ( heat ) is removed.

If a newer system is attempting to achieve integration with an older system which has known flaws ( or " bugs "), then the new system may be referred to as " bugwards-compatible ".

If a system is composed of two subsystems described in V and W respectively, then the Hilbert space of the entire system is the tensor product of the two spaces.

" That rich island ," he wrote on 1 December 1881, " the key to the Gulf of Mexico, is, though in the hands of Spain, a part of the American commercial system … If ever ceasing to be Spanish, Cuba must necessarily become American and not fall under any other European domination.