Since p is prime q − 1 must be a multiple of p. Of course, if the number m = < sup >( q − 1 )</ sup >⁄< sub > p </ sub > is odd, then q will be even, since it is equal to mp + 1.

Since a complete circle has 360 °, 1 < sup > h </ sup > of right ascension is equal to of this, or 15 degrees of arc, 1 < sup > m </ sup > of right ascension is equal to 15 minutes of arc, and 1 < sup > s </ sup > of right ascension is equal to 15 seconds of arc.

Since the most common trailer used in the U. S. is 53 feet ( 16 m ) in length, the difference in freight capacity between cab-over and conventional cab tractor / trailer combinations is negligible.

Since lunch is usually served between 2 and 4 p. m., another common time for tapas is weekend days around noon as a means of socializing before proper lunch at home.

Since the values for drag are based on relative velocity, using the scoop as a form of electromagnetic sail will provide additional thrust as long as the vessel is travelling at less than 500, 000 m / s away from a star.

Since < ƒ, ƒ > ≥ 0, φ ( f * f ) ≥ 0 for all ƒ in L < sup > 2 </ sup >( m ), where ƒ * is pointwise conjugate of ƒ.

Since τ refers to a vertical path, the optical depth for a slant path is τ ′ = m τ, where m is called the relative airmass, and for a plane-parallel

Proof: Since p is a prime number the only possible values of gcd ( p < sup > k </ sup >, m ) are 1, p, p < sup > 2 </ sup >, ..., p < sup > k </ sup >, and the only way for gcd ( p < sup > k </ sup >, m ) to not equal 1 is for m to be a multiple of p. The multiples of p that are less than or equal to p < sup > k </ sup > are p, 2p, 3p, ..., p < sup > k − 1 </ sup > p = p < sup > k </ sup >, and there are p < sup > k − 1 </ sup > of them.

Since ord ( g ) = 0, the element g is invertible in K < nowiki ></ nowiki > X < nowiki ></ nowiki > ⊂ im ( D ) = ker ( Res ), whence Res ( ƒ '/ ƒ ) = m. Property ( iv ): Since ker ( Res ) ⊂ im ( D ), we can write ƒ = ƒ < sub >− 1 </ sub > X < sup >− 1 </ sup > + F ', with F ∈ K (( X )).

Since the construction of the Bukhtarma dam the lake has risen 6 m ( 20 ft ) above its natural level.

Since kinetic energy increases quadratically with velocity (), an object moving at 10 m / s has 100 times as much energy as one of the same mass moving at 1 m / s, and consequently the theoretical braking distance, when braking at the traction limit, is 100 times as long.

Since much of the traffic at the time was between Croydon and Le Bourget Airport in Paris, he proposed the word " Mayday " from the French m ’ aider.

Since October 2010, programming on both night's schedules has been somewhat fluid as while all series have a permanent place on the Friday and Sunday primetime schedules, episode premieres of all Disney Channel original series are subject to being rotated on and off the schedule depending on the schedule for that given week as they usually air as part of a 90-minute block from 8 – 9: 30 p. m. ET / PT on Friday evenings and 7: 30 – 9 p. m. ET / PT on Sunday evenings.

Since Sherman County is part of the Wichita media market and the local broadcast stations are repeat signals of Wichita affiliates, prime-time programming in the county is aired from 6 to 9 p. m. local time, rather than 7 to 10 p. m. as is normal in the Central and Mountain time zones.

Since both k and m are both between 1 and p-1, they must equal.

Since, the inequality could be satisfied for sufficiently small m. The sum of series first converges to the value of φ ( t ) with arbitrary high accuracy if m is small enough, and left part of the strong inequality is satisfied.

* Since m is surjective, we can find b in B such that b ′ =

Since the Supreme Court's decision of that year this is more doubtful ; ;

( Since the time-span of the nation-state coincides roughly with the separate existence of the United States as an independent entity, it is perhaps natural for Americans to think of the nation as representative of the highest form of order, something permanent and unchanging.

Since it is not far from Viareggio, he will visit Puccini's house, as he never fails to do, to pay his respects to the memory of the composer of La Boheme, which he considers one of Puccini's masterpieces.

Since attack serves to stimulate interest in broadcasts, I added to my opening statement a sentence in which I claimed that German youth seemed to lack the enthusiasm which is a necessary ingredient of anger, and might be classified as uninterested and bored rather than angry.

Since the air is a continuum, the network of communication remains intact regardless of the positions or motions of the points ( the people ) in the net.

Since the hazards of poor communication are so great, p can be justified as a habitable site only on the basis of unusual productivity such as is made available by a waterfall for milling purposes, a mine, or a sugar maple camp.

Since the difficulty of drawing the net is great, we will merely discuss it.

Since a civilizational crisis involves also a crisis in private interests and in the ruling class, reaction is normally found among those who feel themselves to be among the ruling class.

Since civilizational change is the most difficult to perceive and analyze, it seldom is given adequate attention.

Since the slogans have little application to reality and are sanctimonious to boot, the applause is faint even in areas of the world where we should expect to find the greatest affection for free government.

Since more is known about Quiney than about any other acquaintance of Shakespeare in Stratford, his career may be followed to its sudden end in 1602.

Since the great flood of these dystopias has appeared only in the last twelve years, it seems fairly reasonable to assume that the chief impetus was the 1949 publication of Nineteen Eighty-Four, an assumption which is supported by the frequent echoes of such details as Room 101, along with education by conditioning from Brave New World, a book to which science-fiction writers may well have returned with new interest after reading the more powerful Orwell dystopia.

Since Laos is of no more purely military value to Moscow itself than it is to Washington, this approach might be expected to head off Mr. Khrushchev for the moment.

Since little is known about autism, and almost nothing has been written for the layman, we'd like to share one experienced mother's comments.

Since the work is done by hand, the only limitation, it is said, `` is that of human conception ''.

Since the apparatus is new, it requires experimentation and changes in technique.

Since the obvious is not always true, the Republican National Committee wisely analyzed its defeat of last autumn and finds that it occurred, as suspected, in the larger cities.

Since he has just shown who is top dog, he may not be ready to receive this highest honor in the gift of the Soviet people.

Since appeals to morality, to humanity, and to sanity have had such small effect, perhaps our last recourse is the deterrent example.

Since the goal of our international planners is a World Government, this Atlantic Community would mark a giant step in that direction for, once American economic autonomy is absorbed, a larger grouping is a question of time.

A set S is called countable if there exists an injective function f from S to the natural numbers Since there is an obvious bijection between and it makes no difference whether one considers 0 to be a natural number of not.

Since the function ƒ is not injective, the relation W is multivalued ( except at 0 ).

* Since q is injective, j ( d )

* Since p is injective, h ( c )

Since η is a ring morphism, then one must have either that A is the trivial ring, or that η is injective.

Since the images φ < sub > n </ sub >( e < sub > k </ sub >( X < sub > 1 </ sub >,…, X < sub > n </ sub >)) = e < sub > k </ sub >( X < sub > 1 </ sub >,…, X < sub > n + 1 </ sub >) for k = 1 ,…, n are still algebraically independent over R, the homomorphism φ < sub > n </ sub > is injective and can be viewed as a ( somewhat unusual ) inclusion of rings.

Since h is a computationally hard-core predicate, recovering h ( x ) from f ( x ) with probability greater than one-half is as hard as inverting f. Perfect binding follows from the fact that f is injective and thus f ( x ) has exactly one preimage.

Since a divisible group is an injective module, Tor ( G ) is a direct summand of G. So

Since f is injective and continuous, it follows that f is a strictly monotonic function, and therefore that the f-mean is neither larger than the largest number of the tuple nor smaller than the smallest number in.

Since any code has to be injective, any two codewords will disagree in at least one position, so the distance of any code is at least.