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Every positive integer is the sum of at most 37 fifth powers ( see Waring's problem ).

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## Some Related Sentences

Every and positive

__Every__non-zero number x, real or complex, has n different complex number nth roots including any

__positive__or negative roots,

**see**complex roots below.

__Every__line

**of**a GEDCOM file begins with a level number where all top-level records

**(**HEAD, TRLR, SUBN, and each INDI, FAM, OBJE, NOTE, REPO, SOUR, and SUBM ) begin with a line with level 0, while other level numbers are

__positive__integers.

*

__Every____positive__**integer**can be written as**the****sum****of**73 or fewer sixth**powers****(****see****Waring's****problem****).**__Every__

__positive__

**integer**can be expressed as

**the**

**sum**

**of**

**at**

**most**19 fourth

**powers**; every sufficiently large

**integer**can be expressed as

**the**

**sum**

**of**

**at**

**most**16 fourth

**powers**

**(**

**see**

**Waring's**

**problem**

**).**

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__C *- algebra has an approximate identity

**of**

__positive__elements

**of**norm ≤ 1 ; indeed,

**the**net

**of**all

__positive__elements

**of**norm ≤ 1 ; in A with its natural order always suffices.

'

__Every____positive__law, or every law simply and strictly so called,**is**set, directly or circuitously, by a sovereign person or body, to a member or members**of****the**independent political society wherein that person or body**is**supreme.__Every__residue class in this group contains exactly one square free

**integer**, and it

**is**common, therefore, only to consider square free

__positive__integers, when speaking about congruent numbers.

Every and integer

*

__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____integer__which can be written as**the****sum****of**two primes, can also be written as**the****sum****of**as many primes as one wishes, until all terms are units.
*

__Every__root**of**a monic polynomial whose coefficients are algebraic integers**is**itself an algebraic__integer__.__Every__memory block in this system has an order, where

**the**order

**is**an

__integer__ranging from 0 to a specified upper limit.

__Every__lattice in can be generated from a basis for

**the**vector space by forming all linear combinations with

__integer__coefficients.

In mathematics, an integer-valued polynomial

**(**also known as a numerical polynomial ) P**(**t )**is**a polynomial whose value P**(**n )**is**an__integer__for every__integer__n.__Every__polynomial with__integer__coefficients**is**integer-valued, but**the**converse**is**not true.
*

__Every__character value**is**a**sum****of**n m < sup > th </ sup > roots**of**unity, where n**is****the**degree**(**that**is**,**the**dimension**of****the**associated vector space )**of****the**representation with character χ and m**is****the**order**of**g. In particular, when F**is****the**field**of**complex numbers, every such character value**is**an algebraic__integer__.__Every__

__integer__instruction could operate on either 1-byte or 2-byte integers and could access data stored in registers, stored as part

**of**

**the**instruction, stored in memory, or stored in memory and pointed to by addresses in registers.

__Every__

__integer__2g ' 2g matrix with < sup >*</ sup > arises as

**the**Seifert matrix

**of**a knot with genus g Seifert surface.

Every and is

__Every__legislator from Brasstown Bald to Folkston

__is__going to have his every vote subjected to

**the**closest scrutiny as a test

**of**his political allegiances, not his convictions.

__Every__detail in his interpretation has been beautifully thought out, and

**of**these I would especially cite

**the**delicious laendler touch

**the**pianist brings to

**the**

**fifth**variation

**(**an obvious indication that he

__is__playing with Viennese musicians ), and

**the**gossamer shading throughout.

__Every__taxpayer

__is__well aware

**of**

**the**vast size

**of**our annual defense budget and

**most**

**of**our readers also realize that a large portion

**of**these expenditures go for military electronics.

__Every__few days, in

**the**early morning, as

**the**work progressed, twenty men would appear to push it ahead and to shift

**the**plank foundation that distributed its weight widely on

**the**Rotunda pavement, supported as it

__is__by ancient brick vaulting.

__Every__dream, and this

__is__true

**of**a mental image

**of**any type even though it may be readily interpreted into its equivalent

**of**wakeful thought,

__is__a psychic phenomenon for which no explanation

__is__available.

__Every__library borrower, or

**at**least those whose taste goes beyond

**the**five-cent fiction rentals, knows what it

__is__to hear

**the**librarian say apologetically, `` I'm sorry, but we don't have that book.

__Every__community, if it

__is__alive has a spirit, and that spirit

__is__

**the**center

**of**its unity and identity.

The restricted principle "

__Every__partially ordered set has a maximal totally ordered subset "__is__also equivalent to AC over ZF.__Every__natural-born citizen

**of**a foreign state who

__is__also an American citizen and every natural-born American citizen who

__is__a citizen

**of**a foreign land owes a double allegiance, one to

**the**United States, and one to his homeland

**(**in

**the**event

**of**an immigrant becoming a citizen

**of**

**the**US ), or to his adopted land

**(**in

**the**event

**of**an emigrant natural born citizen

**of**

**the**US becoming a citizen

**of**another nation

**).**

__Every__line

**of**written text

__is__a mere reflection

**of**references from any

**of**a multitude

**of**traditions, or, as Barthes puts it, "

**the**text

__is__a tissue

**of**quotations drawn from

**the**innumerable centres

**of**culture "; it

__is__never original.

__Every__year, on

**the**last Sunday in April, there

__is__an ice fishing competition in

**the**frozen estuarine waters

**of**

**the**Anadyr River's mouth.

__Every__lattice element

**of**

**the**structure

__is__in its proper place, whether it

__is__a single atom or a molecular grouping.

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