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Every and positive
Every positive integer n > 1 can be represented in exactly one way as a product of prime powers:
Every positive number a has two square roots:, which is positive, and, which is negative.
< li > Every positive definite matrix is invertible and its inverse is also positive definite.
Every positive integer appears exactly once somewhere on this list.
Every positive real number x has a single positive nth root, which is written.
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 rational number can be represented by an Egyptian fraction.
* Every subset of may be covered by a finite set of positive orthants, whose apexes all belong to
* Every positive integer can be written as the sum of 73 or fewer sixth powers ( see Waring's problem ).
Every positive integer is the sum of at most 37 fifth 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 positive rational number can be expanded as an Egyptian fraction.
Every positive integer is the sum of at most 143 seventh powers ( see Waring's problem ).
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 positive rational number q may be expressed as a continued fraction of the form

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 real number, whether integer, rational, or irrational, has a unique location on the line.
: Every even integer greater than 2 can be expressed as the sum of two primes.
: 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 integer greater than 2 can be written as the sum of three primes.
: Every integer greater than 5 can be written as the sum of three primes.
: Every even integer greater than 2 can be written as the sum of two primes,
* 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 integer greater than 96 may be represented as a sum of distinct super-prime numbers.
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 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 twin prime pair except ( 3, 5 ) is of the form ( 6n − 1, 6n + 1 ) for some natural number n, and with the exception of < var > n </ var > = 1, < var > n </ var > must end in 0, 2, 3, 5, 7, or 8.
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 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 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.

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