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Furthermore, if b < sub > 1 </ sub > and b < sub > 2 </ sub > are both coprime with a, then so is their product b < sub > 1 </ sub > b < sub > 2 </ sub > ( modulo a it is a product of invertible elements, and therefore invertible ); this also follows from the first point by Euclid's lemma, which states that if a prime number p divides a product bc, then p divides at least one of the factors b, c.
Some Related Sentences
Furthermore and if
Furthermore, each individual speaker has their own style of signing depending on various factors, such as where they went to school, if they were mainstreamed ( see Mainstreaming ( education )), who taught them ASL, at what age they learned ASL, and how active they are in the Deaf Community.
Furthermore, if the Soviets chose to enter this new arms race, they would further cripple their economy.
Furthermore, a map f: A → B is a homomorphism of Boolean algebras if and only if it is a homomorphism of Boolean rings.
Furthermore, for every a ∈ A we have that a ∧-a = 0 ∈ I and then a ∈ I or-a ∈ I for every a ∈ A, if I is prime.
Furthermore, Pasternak was informed that, if he traveled to Stockholm to collect his Nobel Medal, he would be refused re-entry to the Soviet Union.
Furthermore, the director's contract of service will usually entitle him to compensation if he is removed, and may often include a generous " golden parachute " which also acts as a deterrent to removal.
Furthermore, the wood is often so porous, that if the varnish is stripped off the inexpensive bokken, one can see the use of wood fillers to fill the holes.
Furthermore, if we flat bet at 10 units per round instead of 1 unit, the range of possible outcomes increases 10 fold.
Furthermore, even if the calendar is very accurate, its accuracy diminishes slowly over time, owing to changes in Earth's rotation.
Furthermore, the history of a number of ongoing experiments in multiculturalism, such as in the European Union, India, South Africa, Canada and the United States, suggests that workable, if not perfected, integrative models exist.
Furthermore, even if one chooses to accept God as the First Cause, there is an argument that God's continued interaction with the Universe is not required.
Furthermore Demea states that even if the succession of causes is infinite, the whole chain still requires a cause.
Furthermore, if the same device with no explicit performance specs beyond the Compact Disc logo initially handles nonstandard discs reliably, there is no assurance that it will not later stop doing so, and in that case, there is no assurance that it can be made to do so again by service or adjustment.
Furthermore, if the Lieutenant Governor becomes incapacitated while serving in the office of Governor, the next most senior judge of the Supreme Court is sworn in as the Administrator.
Furthermore, imports into the EC are possible from third countries if the irradiation facility had been inspected and licensed by the EC and the treatment is legal within the EC or some Member state.
Furthermore, as mentioned above, frequentist analysis is open to unscrupulous manipulation if the experimenter is allowed to choose the stopping point, whereas Bayesian methods are immune to such manipulation.
Furthermore, if the language is translated, the translator has room to shift a bias by choosing weighed words for translation.
Furthermore, the act provided that any bill rejected by the Lords would nevertheless become law if passed by the Commons in three successive sessions provided that two years had elapsed since its original passage.
Furthermore, in many works of fiction a rifle refers to any weapon that has a stock and is shouldered before firing, even if the weapon is not rifled or does not fire solid projectiles ( e. g. a " laser rifle ").
Furthermore, if a network server is highly loaded with network traffic, its response time may be slower but will ( in most cases ) still succeed before it times out ( hits its deadline ).
Furthermore and b
Furthermore, RS codes are suitable as multiple-burst bit-error correcting codes, since a sequence of b + 1 consecutive bit errors can affect at most two symbols of size b.
Furthermore, if the morphism f is a monomorphism, then so is the morphism ker a → ker b, and if g is an epimorphism, then so is coker b → coker c.
Furthermore, the admissibility of expert testimony is governed by Rule 104 ( a ), not Rule 104 ( b ); thus, the Judge must find it more likely than not that the expert's methods are reliable and reliably applied to the facts at hand.
Furthermore, stage ( b ) corresponds to Chris Alexander's " tree " city, while ( c ) is similar to his " lattice " system ( following his dictum " the city is not a tree ").
Furthermore, | f ( b < sub > k </ sub >)| should be less than or equal to | f ( a < sub > k </ sub >)|, so that b < sub > k </ sub > is a better guess for the unknown solution than a < sub > k </ sub >.
Furthermore, proved that the predecessor relation gives rise to a complete lattice when restricted to the set of minimal ( a, b )- separators in G.
Furthermore, increases in assessment shall not exceed the lower of: a ) 3 % of assessed value from prior year ; or b ) percentage change in CPI.
Furthermore, the site has no system of checking and verifying the a ) truthfulness of the fact that the post is by a genuine student / pupil and b ) the truthfulness of the account of the teacher's ability.
Furthermore, the act stated in section 3 ( b ) that if misappropriation is, " willful and malicious " the court may award damages up to twice what would otherwise be entitled under section 3 ( a ).
Furthermore and <
Furthermore, while Neuromancer < nowiki >'</ nowiki > s narrator may have had an unusual " voice " for science fiction, much older examples can be found: Gibson's narrative voice, for example, resembles that of an updated Raymond Chandler, as in his novel The Big Sleep ( 1939 ).
Furthermore, all solutions x of this system are congruent modulo the product, N = n < sub > 1 </ sub > n < sub > 2 </ sub >… n < sub > k </ sub >.
Furthermore, Oman presents in its stratigraphic record a large negative carbon isotope excursion, within the Shuram Formation that is clearly away from any glacial evidence < ref name = LeGuerroue2006b >
Furthermore, these two probabilities are equally as likely as any other 21-flip combinations that can be obtained ( there are 2, 097, 152 total ); all 21-flip combinations will have probabilities equal to 0. 5 < sup > 21 </ sup >, or 1 in 2, 097, 152.
Furthermore, aside from helium and hydrogen, it is the least dense element in a solid or liquid state, being only 2 / 3 as dense as liquid nitrogen ( 0. 808 g / cm < sup > 3 </ sup >).
Furthermore, whenever p is a Sophie Germain prime — that is, 2p + 1 is also prime — and 2p + 1 is congruent to 1 or 7 mod 8, then 2p + 1 will be a factor of 2 < sup > p </ sup >− 1.
Furthermore, insulating materials such as silicon dioxide ( SiO < sub > 2 </ sub >), when exposed to photons with energy greater than the band gap, release free electrons and holes which subsequently cause adverse charging.
Furthermore, for mathematicians, according to this formula the gluon color field can be represented by a SU ( 3 )- Lie algebra-valued " curvature "- 2-form where is a " vector potential "- 1-form corresponding to G and is the ( antisymmetric ) " wedge product " of this algebra, producing the " structure constants " f < sup > abc </ sup >.
Furthermore, the net potential difference of the galactic electric field in interstellar space is only 1. 6 × 10 < sup >− 19 </ sup > volt.
Furthermore, this fixed point can be found as follows: start with an arbitrary element x < sub > 0 </ sub > in X and define an iterative sequence by x < sub > n </ sub >
Furthermore, maximal ideals can be generalized by defining a maximal sub-bimodule M of a bimodule B to be a proper sub-bimodule of M which is contained by no other proper sub-bimodule of M. So, the maximal ideals of R are exactly the maximal sub-bimodules of the bimodule < sub > R </ sub > R < sub > R </ sub >.
Furthermore, the strict relations < and > are of little use in many non-total orders and hence no additional terminology is introduced for them.
Furthermore, MgB < sub > 2 </ sub > superconducts at temperatures higher than LTS ( its critical temperature is 39 K, compared with less than 10 K for NbTi and 18. 3 K for Nb < sub > 3 </ sub > Sn ), introducing the possibility of using it at 10-20 K in cryogen-free magnets or perhaps eventually in liquid hydrogen.
Furthermore, the conductivity can undergo a quantization in energy: i. e. the energy of the electrons going through a nanowire can assume only discrete values, which are multiples of the Von Klitzing constant G = 2e < sup > 2 </ sup >/ h ( where e is the charge of the electron and h is the Planck constant ).