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Some Related Sentences
Every and prime
Every positive integer
n > 1 can be represented
in exactly one way as a product
of prime powers:

Hilbert's example: "
the assertion that either there are only finitely many
prime numbers
or there are infinitely many "
( quoted
in Davis 2000: 97 );
and Brouwer's: "
Every mathematical species
is either finite
or infinite
.
Every completely multiplicative function
is a homomorphism
of monoids
and is completely determined by its restriction to
the prime numbers
.

* In any ring R
, a maximal ideal
is an ideal M that
is maximal
in the set
of all proper ideals
of R
, i
. e
. M
is contained
in exactly
2 ideals
of R
, namely M itself
and the entire ring R
. Every maximal ideal
is in fact
prime.

#
Every prime ideal
of A
is principal
.
Every third odd
number is divisible by
3, which requires that no three successive odd numbers can be
prime unless one
of them
is 3.

* Hardy
and Littlewood listed as their Conjecture I: "
Every large odd
number ( n > 5 ) is the sum
of a
prime and the double
of a
prime.
Every prime ideal P
in a Boolean ring R
is maximal:
the quotient ring R / P
is an integral domain
and also a Boolean ring
, so it
is isomorphic to
the field F
< sub
> 2 </ sub >, which shows
the maximality
of P
. Since maximal ideals are always
prime, prime ideals
and maximal ideals coincide
in Boolean rings
.
Every strong probable
prime to base a
is also an Euler probable
prime to
the same base
, but not vice versa
.
Every closed 3-manifold has a
prime decomposition: this means it
is the connected sum
of prime three-manifolds
( this decomposition
is essentially unique
except for a small problem
in the case
of non-orientable manifolds ).

:
Every oriented
prime closed 3-manifold can be cut along tori
, so that
the interior
of each
of the resulting manifolds has a geometric structure
with finite volume
.
Every non-zero characteristic
is a
prime number.

:
Every Boolean algebra contains a
prime ideal
.

*
Every number of the form 2 < sup
> m
</ sup
> p
for a
natural number m
and a
prime number p such that p
< 2 < sup
> m
+ 1 </ sup
> is also semiperfect
.
Every group
of prime order
is cyclic
, since Lagrange's theorem implies that
the cyclic subgroup generated by

Iwasawa worked
with so-called-extensions: infinite extensions
of a
number field
with Galois group isomorphic to
the additive group
of p-adic integers
for some prime p
. Every closed subgroup
of is of the form, so by Galois theory
, a-extension
is the same thing as a tower
of fields such that
.
Every imperfect field
is necessarily transcendental over its
prime subfield
( the minimal subfield ), because
the latter
is perfect
.

A finitely-generated abelian group
is indecomposable if
and only if it
is isomorphic to Z
or to a factor group
of the form for some prime number p
and some positive integer
n. Every finitely-generated abelian group
is a direct sum
of ( finitely many
) indecomposable abelian groups
.

*
Every non-split
, prime, alternating link that
is not a torus link
is hyperbolic by a result
of William Menasco
.
Every and pair
Every ATM cell has an 8-or 12-bit Virtual Path Identifier
( VPI
) and 16-bit Virtual Channel Identifier
( VCI
) pair defined
in its header
.

*
Every pair of congruence relations
for an unknown integer x
, of the form x ≡ k
( mod a
) and x ≡ l
( mod b ), has a solution
, as stated by
the Chinese remainder theorem ;
in fact
the solutions are described by a single congruence relation modulo ab
.
Every pair of points belongs to a unique line
.
Every Saturday night
, from 1995 to 2000
, he would host a
pair of horror films
( such as Friday
the 13th Part
2 and Wes Craven's New Nightmare
) provide a running commentary
, trivia
, off-color jokes
and a drive-in total
.

This
pair of brothers later wrote a book entitled Foot by Foot Through
the USA
, A High Adventure Odyssey To
Every State
in the Union
, which chronicled their journey
.
Every constraint
is in turn a
pair ( usually represented as a matrix ), where
is an-tuple
of variables
and is an-ary relation on
.
Every minimal
pair of natural numbers has
and, for otherwise
the pair would belong to
and be at least as small
in both coordinates
, contradicting
the assumption that
is minimal
.
Every pair of MojoNation nodes maintained a relative credit balance
, with every EGTP request transferring
some Mojo credit from
the sender to
the receiver
.
Every pair of colors appears on at least one edge
.
Every Wednesday
the pair write about everything from summer holidays to sexy ladies
.
Every point
in the training
is an input-output
pair, where
the input
Every pair plays against a
number of opposing pairs
in successive rounds
, depending on
the size
of the field
.
Every homeroom
is led by a
pair of teachers
with combined native language abilities
in both English
and Mandarin
, and at every year level
, teachers
of the two languages collaborate to plan
and teach outcomes from
the school's inquiry-based integrated program
.

*
Every pair of distinct points determines a unique line
.
Every matched
pair of threads
, external
and internal
, can be described as male
and female
.

Knopfler performed " Money
for Nothing " using his Pensa-Suhr signature MK-1 model guitar
with a
pair of Soldano SLO-100 tube / valve amplifier heads
and Marshall speaker cabinets during
the Nelson Mandela 70th Birthday Tribute
and Prince's Trust concerts
in 1988
, as well as
the Nordoff-Robbins charity show at Knebworth
in 1990
and the On
Every Street world tours
in 1991 / 1992
.
Every pair of balls
( Hamming spheres
) are non-intersecting by
the t-error-correcting property
, and each ball contains
( in other words
, the volume
of the ball
) m words
.

As described
in an article
in the London newspaper
, The Daily Courier
, on June 25
, 1896: "
Every one who has watched a bout
with the foils knows that
the task
of judging
the hits
is with a
pair of amateurs difficult enough
, and with a well-matched
pair of maîtres d ’ escrime well-nigh impossible
.
Every pair of points are i
< sup
> th
</ sup
> associates
for exactly one
.
Every convex centrally symmetric polyhedron P
in R
< sup
> 3 </ sup
> admits a
pair of opposite
( antipodal
) points
and a path
of length L joining them
and lying on
the boundary ∂ P
of P
, satisfying
Every complex
number has both a real part
and an imaginary part
, so one complex variable
is two-dimensional
and a
pair of complex variables
is four-dimensional
.
Every and except
Every member
of the future protectionist cabinet then
in parliament
( except Disraeli
) voted against
the measure
.
Every action specifically intended to prevent procreation
is forbidden
, except in medically necessary circumstances
.
Every president since Taft
, except for Jimmy Carter
, threw out at least one ceremonial first ball
or pitch
for Opening Day
, the All-Star Game
, or the World Series
, usually
with much fanfare
.
Every S / 360
( except for the Model 20
, which was not a standard S / 360
) had a byte-multiplexer channel
and 1 or more selector channels
.
Every element s
, except a possible greatest element
, has a unique successor
( next element ), namely
the least element
of the subset
of all elements greater than s
. Every subset which has an upper bound has a least upper bound
.
Every album
, except 1969's The Chicago Transit Authority
, 1978's Hot Streets
and 1995's Night
and Day: Big-Band
, released by Chicago Transit Authority / Chicago has been
the band name followed by a Roman numeral
or numbered
in some other manner
.
Every state
except Nebraska has a bicameral legislature
, meaning that
the legislature consists
of two separate legislative chambers
or houses
.
Every deity
and demi-god had been invited
, except Eris
, the goddess
of strife
( no one wanted a troublemaker at a wedding ).
Every book
in the Hebrew Bible was represented
in this discovery
except Esther
.
Every corn-growing country decided to increase tariffs
in reaction to this
, except Britain
and Belgium
.
Every British North Atlantic route was suspended until 1856
except Cunard's Liverpool-Halifax-Boston service
.
Every evening since 1928
( except for a period during
the Second World War when Ypres was occupied by Germany ), at precisely eight o ' clock
, traffic around
the imposing arches
of the Menin Gate Memorial has been stopped while
the Last Post
is sounded beneath
the Gate by
the local fire brigade
.
Every body panel
, except for the doors
, were redesigned
.
Every sequence
in principle has a generating function
of each type
( except that Lambert
and Dirichlet series require indices to start at
1 rather than
0 ), but
the ease
with which they can be handled may differ considerably
.
Every day had
the name
of an agricultural plant
, except the 5th
( Quintidi
) and 10th day
( Decadi
) of every decade
, which had
the name
of a domestic animal
( Quintidi
) or an agricultural tool
( Decadi ).
Every episode
except one featured a live performance by a band
, including Madness
, Motörhead
, and The Damned
.
Every century
except the 21st has seen major building work
or adaptations at
the castle
.
Every state
, except Arkansas
and Mississippi
, maintains a state FEPA
( see EEOC
and state FEPA directory ).

*
Every real
number greater than zero
or every complex
number except 0 has two square roots
.
Every day had
the name
of an agricultural plant
, except the 5th
( Quintidi
) and 10th day
( Decadi
) of every decade
, which had
the name
of a domestic animal
or an agricultural tool
, respectively
.
Every song features Carly Simon singing
except for ' The More It Snows
( Tiddely-Pom )'.
Every province
in Canada
except Alberta has either a Provincial Sales Tax
( PST
) or the Harmonized Sales Tax
( HST ), which
is a single
, blended combination
of the GST
and PST
.
1.511 seconds.