Fortunately, faster methods have been developed which require only O ( p ( log p )< sup > 2 </ sup >) operations ( see big-O notation ).

Assume p and q − 1 are relatively prime, a similar application of Fermat's Little Theorem says that ( q − 1 )< sup >( p − 1 )</ sup > ≡ 1 ( mod p ).

Thus there is a number x ≡ ( q − 1 )< sup >( p − 2 )</ sup > for which ( q − 1 )· x ≡ 1 ( mod p ), and therefore a number k for which ( q − 1 )· x − 1 = kp.

The discrepancy is a factor of 2. 4 ― 4. 3 below the theoretically predicted value and is considered a problem for the original models, that have resulted in revised calculations of the standard BBN based on new nuclear data, and to various reevaluation proposals for primordial proton-proton nuclear reactions, especially the intensities of < sup > 7 </ sup > Be ( n, p )< sup > 7 </ sup > Li versus < sup > 7 </ sup > Be ( d, p )< sup > 8 </ sup > Be.

: K < sub > sp </ sub > = < sup > p </ sup > ( q / p )< sup > q </ sup > < sup > q </ sup >

:=( q / p )< sup > q </ sup > × < sup > p + q </ sup >

: ( 2D )< sup > 2 </ sup > = d < sup > 2 </ sup >( 1 + cos α )< sup > 2 </ sup > + p < sup > 2 </ sup >

Suppose λ is a root of p ( t ) having multiplicity r. This is to say that ( t − λ )< sup > r </ sup > divides p ( t ).

Dividing p ( x ) by ( x − 1 )< sup > 2 </ sup >, we get p ( x ) = ( x + 3 )( x − 1 )< sup > 2 </ sup > so the other root is − 3, a single root.

via the identity ( p + q )< sup > 2 </ sup >-( p-q )< sup > 2 </ sup > =

* If it is required to use a single number X as an estimate for the value of numbers, then the arithmetic mean does this best, in the sense of minimizing the sum of squares ( x < sub > i </ sub > − X )< sup > 2 </ sup > of the residuals.

Egyptian civilization coalesced around 3150 BC ( according to conventional Egyptian chronology )< ref >

To see the elongated shape of ψ ( x, y, z )< sup > 2 </ sup > functions that show probability density more directly, see the graphs of d-orbitals below.

An amide is a compound with the functional group R < sub > n </ sub > E ( O )< sub > x </ sub > NR '< sub > 2 </ sub > ( R and R ' refer to H or organic groups ).

The term amide refers both to classes of compounds and to the functional group ( R < sub > n </ sub > E ( O )< sub > x </ sub > NR '< sub > 2 </ sub >) within those compounds.

* Equate – Al ( OH )< sub > 3 </ sub > and Mg ( OH )< sub > 2 </ sub >

Also, more readily reacting raw materials may be preferred over relatively inert ones, such as Al ( OH )< sub > 3 </ sub > over Al < sub > 2 </ sub > O < sub > 3 </ sub >.

Also, Demon X ( A / N )< sup > th </ sup > has made a deal with Demon JU ( P / I )< sup > ter </ sup > that he could get one Xanthian to shed

Randomized algorithms can solve the problem in O (( log n )< sup > 2 </ sup >) time on processors ( note this is superpolynomial ).

The average separation between the triton and the deuteron in the electronic molecular ion is about one angstrom ( 100 pm ),< ref name =" Jackson ">< ref group =" note "> According to, footnote 16, Jackson may have been overly optimistic in Appendix D of his 1957 paper in his roughly calculated " guesstimate " of the rate of formation of a muonic ( p-μ-p )< sup >+</ sup > molecular ion by a factor of about a million or so.

note that the Standard Model fermion fields ( including the right handed neutrinos ) come from all three × U ( 1 )< sub > B </ sub >/ Z < sub > 5 </ sub > representations.

To see this, note that with a 16 < sub > 1H </ sub > and a Higgs field, we can have VEVs which breaks the GUT group down to × U ( 1 )< sub > χ </ sub >/ Z < sub > 4 </ sub >.

Telephone lines in use: 3, 9741 million ( 2011 )< BR />

The current aim is to use the reaction < sup > 226 </ sup > Ra (< sup > 48 </ sup > Ca, 4n )< sup > 270 </ sup > Hs.

To define the vector space operations on T < sub > x </ sub > M, we use a chart φ: U → R < sup > n </ sup > and define the map ( dφ )< sub > x </ sub >: T < sub > x </ sub > M → R < sup > n </ sup > by ( dφ )< sub > x </ sub >( γ '( 0 )) = ( φ ∘ γ )'( 0 ).

A more rigorous presentation would use the expression (− 1 )< sup > n </ sup >, which gives + 1 when n is even and − 1 when n is odd.

Next, we can use Euler's formula to obtain a real sinusoid with amplitude I < sub > 0 </ sub >, angular frequency ω < sub > 0 </ sub > = ( LC )< sup >− 1 / 2 </ sup >, and phase angle.

( This area of Saint Mark's is simply empty space in GTAIII and GTA: LCS )< ref name =" GTASA Liberty City access "> Players have learned to access Grand Theft Auto: San Andreas < nowiki >'</ nowiki > s incomplete Liberty City or venture beyond the limited bounds of the mission in multiple methods through the use of trainers or cheat codes .</ ref >

Those that use cinders ( fly ash or bottom ash ) are called cinder blocks in Canada, the US and New Zealand, breeze blocks ( breeze is a synonym of ash )< ref > in the UK and are also known as besser blocks or bricks in Australia.

The above identities use the number i to remove the alternating factor (− 1 )< sup > n </ sup > from terms of the series to restore the full halves of the exponential series.

The catalyst is prepared in situ from ( i-PrO )< sub > 2 </ sub > TiX < sub > 2 </ sub > and optically pure binaphthol, the alkoxy-ligand exchange being facilitated by the use of molecular sieves.

* Molybdenum disilicide doped with Al or Mo ( Si, Al )< sub > 2 </ sub >, an intermetallic compound and a silicide of molybdenum, is a refractory ceramic with primary use in heating elements.

Puriri trees or groves were often tapu through their use as burial sites < sup >( 15 )</ sup > and puriri leaves were fashioned in to coronets or carried in the hand during a tangi ( funeral )< sup >( 6 )</ sup >.

Combinatorialists use the Pochhammer symbol ( x )< sub > n </ sub > to denote the falling factorial

The inorganic composition of bone ( bone mineral ) is formed from carbonated hydroxyapatite ( Ca < sub > 10 </ sub >( PO < sub > 4 </ sub >)< sub > 6 </ sub >( OH )< sub > 2 </ sub >) with lower crystallinity.

Spinel, ( Mg, Fe )( Al, Cr )< sub > 2 </ sub > O < sub > 4 </ sub >, is common in peridotite in the uppermost Earth's mantle, between approximately 20 km to approximately 120 km, possibly to lower depths depending on the chromium content.

is the " falling factorial " or " lower factorial ", while the empty product ( x )< sub > 0 </ sub > is defined to be 1.

The probability that 100 randomly typed keys will consist of the first 99 digits of pi, or any other particular sequence, is much lower: ( 1 / 90 )< sup > 100 </ sup >.

They all have lower energy than the lowest-energy intense band for the Fe ( II ) complex Fe ( CN )< sub > 6 </ sub >< sup > 2 -</ sup > found at 46000 cm < sup >− 1 </ sup >.

Pór and Wood ( 2005 ) give a lower bound of Ω (( rn )< sup > 3 / 4 </ sup >) on the volume of any three-dimensional grid embedding of the Turán graph.

At lower salt concentrations, the ( SSB )< sub > 35 </ sub > binding mode, in which about 35 nucleotides bind to only two of the SSB subunits, tends to form.

As a consequence, since kinetic energy is equal to 1 / 2 ( mass )( velocity )< sup > 2 </ sup >, the heavier atoms of xenon have a lower average speed than do the lighter atoms of helium at the same temperature.

Finding matching upper and lower bounds for the complexity of a k-level remains a major open problem in discrete geometry ; the best upper bound is O ( nk < sup > 1 / 3 </ sup >), while the best lower bound is Ω ( n exp ( c ( logk )< sup > 1 / 2 </ sup >)).