* 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 positive integer n > 1 can be represented in exactly one way as a product of prime powers:

: 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 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 positive integer appears exactly once somewhere on this list.

* 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 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 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.

* Every positive integer except 1 is a PV number.

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 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 ).

* 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.

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 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.

Disraeli wrote a personal letter to Gladstone, asking him to place the good of the party above personal animosity: " Every man performs his office, and there is a Power, greater than ourselves, that disposes of all this ..." In responding to Disraeli Gladstone denied that personal feelings played any role in his decision then and previously to accept office, while acknowledging that there were differences between him and Derby " broader than you may have supposed.

This was to be based on utilitarian principles ; he said: " Every man has a right to that, the exclusive possession of which being awarded to him, a greater sum of benefit or pleasure will result than could have arisen from its being otherwise appropriated.

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 aspect of the line matrix printer is designed to deliver higher reliability, fast throughput, and greater resistance to rough handling and hazardous environmental conditions.

: Every odd number greater than 7 can be expressed as the sum of three odd primes.

Every Balangay that did not gain Sanggunian Bayan status were dissolved and annexed by greater provincial or popular councils.

* Every real number greater than zero or every complex number except 0 has two square roots.

Every structure is associated with a certain quantity of energy, which determines the stability of the molecule or ion ( the lower energy, the greater stability ).

Boateng played a leading role in coordinating the Every Child Matters policy paper, which called for the reform of children's services, including greater accountability and coordination among government agencies.

Every year, several pieces are chosen from the greater Houston area to be produced.

Every man must serve another's larger cause, giving or lending himself in whole or in part to another judgement, a further condition, a greater good, a lesser will, a common motive and purpose, and these replace his own criteria, the immediacy of his own conscience, until his own moral nature becomes a mere accessory to the cause, which is no more than his neighbour's, but the product of some ill-defined greater good and lesser evil.

Every man entered the contest intending not just to look good, but to survive, and to come away from the field worthy of greater respect.

Every number greater than 0. 3 is considered a " not kill ".

* Every individual will have a responsibility to contribute back to the greater natural and social community from his / her Brown School experience.

# Every node of level greater than one has two children.

Every state other than Vermont has a balanced budget amendment, providing some form of ban on deficits, while the Oregon kicker bans surpluses of greater than 2 % of revenue.

Every pipe or vessel is subject to heat loss when its temperature is greater than ambient temperature.

Every universe is covered by seven layers — earth, water, fire, air, sky, the total energy and false ego — each ten times greater than the previous one.

** Every unital ring other than the trivial ring contains a maximal ideal.

* Every topological space X is a dense subspace of a compact space having at most one point more than X, by the Alexandroff one-point compactification.

Every contraction mapping is Lipschitz continuous and hence uniformly continuous ( for a Lipschitz continuous function, the constant k is no longer necessarily less than 1 ).

Every other aspect of film making originated in a different medium than film ( photography, art direction, writing, sound recording ), but editing is the one process that is unique to film.

The work is much more accessible than Sana ’ i ’ s for instance ; " Every line of the Rubaiyat has more meaning than almost anything you could read in Sufi literature ".

Every aspect of the collage is moving and will never be the same more than once, which was congruent with society at the time.

In Anime Essentials: Every Thing a Fan Needs to Know, Giles Poitras wrote " More humorous and less serious looking than the characters in the Lodoss War series, the stars of Slayers provide action and laughs ".

Every new emperor after him was honored by the Senate with the wish felicior Augusto, melior Traiano (" luckier than Augustus and better than Trajan ").

Every day, there are more than one million vehicles travelling within the city.

Every day, doors seem to open, and every day, we interact, perhaps more than ever before, with the world outside.

In the autumn of 1970 Jurgen Wischnewski of the SPD declared, ‘ Every week more than three plans for reform come up for decision in cabinet and in the Assembly .’ ”

The Body of Liberties adopted in 1641 by the Massachusetts Bay colonists states, “ Every married woman shall be free from bodily correction or stripes by her husband, unless it be in his own defense from her assault .” In the United States, legal decisions in Mississippi ( 1824 ) and North Carolina ( 1868 and 1874 ) make reference to — and reject — an unnamed " old doctrine " or " ancient law " by which a man was allowed to beat his wife with a stick no wider than his thumb.

* Every rule of thumb on earth in one place-A user participation reference project based on Tom Parker's 3 best-selling books and more than 25 years of research.

Every material has its own characteristic resistivity — for example rubber's resistivity is far larger than copper's.