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 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 except 1 is a PV number.

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 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.

George Every discusses the connection between the cosmic center and Golgotha in his book Christian Mythology, noting that the image of Adam's skull beneath the cross appears in many medieval representations of the crucifixion.

Every domain name appears in a zone served by one or more authoritative name servers.

Every cycle climaxes in the arrival of The Leveler, whose approach ( and fall ) is heralded by an ominous comet that appears in the sky.

Every time Harold tries to switch places with Bill, the policeman appears and chases Bill away.

* Every write operation appears to occur instantaneously

In the scene, Vesper appears for the first time introducing herself with " I'm the money " ( referring to her role as a Treasury accountant ), to which Bond replies, while looking her over, " Every penny of it.

In 1985, on an episode of " Too Close For Comfort " entitled " For Every Man There's Two Women "( S05, E10 ), Ted Knight ( playing Henry Rush ) appears on the episode wearing a Fairleigh Dickinson University maroon sweatshirt.

Every house appears to have siding on it.

Every pair of colors appears on at least one edge.

The Road to Serfdom appears on Martin Seymour-Smith's list of the 100 Most Influential Books Ever Written, whilst it made # 1 on Human Events: Top Ten Books Every Republican Congressman Should Read in 2006.

Every cycle climaxes in the arrival of The Leveler, whose approach ( and fall ) is heralded by an ominous comet that appears in the sky.

" Every creature, every work of God, is admirably well made ; but if any one appears imperfect in our eyes, it does not belong to us to criticise it.

Local reaction to the Grantham Journal was over-ridingly negative with vehement criticism in the letters page including " Because he is one of Cameron ’ s Cronies, he appears to believe that he can get away with absolutely anything. Every time this man opens his mouth, he spouts utter drivel, Why couldn ’ t the Tory selectors have sent us a Genghis Khan figure, not this useless lightweight?

It appears on his 2001 CD A Live One and, in reference to his efforts to rid himself of thoughts and memories of a previous lover, contains the line " Every night I see your face when I have to pray.

Every time he appears on television, he says something along the following lines.

" Et tu, Brute " occurs in V, iv of Every Man Out ; in III, i appears " reason long since is fled to animals ," a paraphrase of Shakespeare's line " O judgment, thou art fled to brutish beasts " in Julius Caesar, III, ii, 104.

Every three months, the President of the ECB, or occasionally his deputy, appears before the Committee to report on monetary policy ; both actions taken, and future prospects.

* Angry Patrick-Patrick appears on Fridays after the Week in Review ( see below ) to rant about current events in pop culture that are bothering him. He even has a little jingle they start him off with. Every week, he also uses his iconic phrase -" ARE YOU FREAKIN ' KIDDING ME?

In fact, the phrase next appears in a book of Scottish proverbs published in 1721, in the form " Every Man is no born with a Silver Spoon in his Mouth.