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{{Short description|Inequality relating the primorial to square of the next prime number}} .../sub>, ''p''_''n''+1 are the smallest ''n'' + 1 [[prime number]]s and ''n'' ≥ 4, then ...

...orem''' is a theorem in [[number theory]] concerning the distribution of [[prime number]]s. It is named after [[Paul Erdős]] and Hubert Delange. ...ymptotically uniformly distributed modulo 1.{{r|delange}} It implies the [[prime number theorem]].{{r|bergelson-richter}} ...

{{Short description|Theorem about prime numbers}} ...' is a theorem due to [[Helmut Maier]] about the numbers of [[Prime number|prime]]s in short intervals for which [[Cramér model|Cramér's probabilistic model ...

...er bound]] on the distribution of [[primes in arithmetic progression|prime numbers in arithmetic progression]]. ...Motohashi|first=Yoichi|authorlink=Yoichi Motohashi|title=Sieve Methods and Prime Number Theory|publisher=Tata IFR and Springer-Verlag|year=1983|isbn=3-540-1 ...

...ith finitely many prime factors necessarily introduces infinitely many new prime factors.<ref name="kobayashi">{{cite journal | title = On Existence of Infinitely Many Prime Divisors in a Given Set ...

...description|On the divisibility of solutions to Fermat's Last Theorem for prime exponent}} ...equation <math>x^p + y^p = z^p</math> of [[Fermat's Last Theorem]] for odd prime <math>p</math>. ...

...ly in many theorems in [[number theory]]. The following are a few of these theorems.<ref name=MAA/> ..., a polynomial in which the coefficients are integers and are [[relatively prime]] to each other. If the degree of ''f''(''x'') is ''k'' then the [[greatest ...

...400px|[[Hasse diagram]] of the [[lattice (order)|lattice]] of supernatural numbers; primes other than 2 and 3 are omitted for simplicity.]] ...bers''', sometimes called '''generalized natural numbers''' or '''Steinitz numbers''', are a generalization of the [[natural number]]s. They were used by [[Er ...

...nd the relations).<ref>{{harvnb|Procesi|2007|loc=Ch. 9, § 1.4.}}</ref> The theorems are among the most important results of [[invariant theory]]. ...haracteristic (algebra)|characteristic]]-free invariant theory extends the theorems to a [[field (mathematics)|field]] of arbitrary characteristic.<ref>{{harvn ...

...[[number fields]], i.e., finite [[field extension]]s ''K'' of the rational numbers '''Q''', such that the [[discriminant of an algebraic number field|discrimi ...''Q''' is not ±1, which in turn implies that '''Q''' has no [[Splitting of prime ideals in Galois extensions|unramified]] extensions. ...

...istributed equally across possible progressions with the same difference. Theorems of the Barban–Davenport–Halberstam type give estimates for the error term, ...057 | last=Hooley | first=C. | author-link=Christopher Hooley | chapter=On theorems of Barban-Davenport-Halberstam type | pages=75–108 | editor1-last=Bennett | ...

{{About|a theorem in number theory||Hurwitz's theorem (disambiguation){{!}}Hurwitz' ...nal number]] ''ξ'' there are infinitely many [[coprime integers|relatively prime]] integers ''m'', ''n'' such that ...

{{short description|Characterization of even perfect numbers}} ...perfect numbers and Mersenne primes|the theorem on the infinitude of prime numbers|Euclid's theorem}} ...

...technique introduced by [[Alexander Grothendieck]] for proving statements about [[coherent sheaf|coherent sheaves]] on [[noetherian scheme]]s. Dévissage is ...coherent ''O''_''X''-module whose support is contained in ''X''&prime; is contained in '''C'''.<ref>EGA III, Théorème 3.1.2</ref> ...

...escription|Result in number theory showing congruences involving Bernoulli numbers}} ...nces''' are some [[Congruence relation|congruence]]s involving [[Bernoulli numbers]], found by {{harvs|txt|authorlink=Ernst Eduard Kummer|first=Ernst Eduard|l ...

{{short description|Characterization by prime factors of sums of two squares}} In [[number theory]], the '''sum of two squares theorem''' relates the [[prime decomposition]] of any [[integer]] {{math|{{var|n}} > 1}} to whether it can ...

...''K^s''. Given a finite ''G_K''-module ''A'' of order prime to the [[characteristic (algebra)|characteristic]] of ''K'', the Tate dual :<math>A^\prime=\mathrm{Hom}(A,\mu)</math> ...

...tegers]] of ''K''. Tate's result then states that if ''m'' is [[relatively prime]] to the [[characteristic (algebra)|characteristic]] of ''K'', then<ref>{{h ...one. If ''K'' is a [[finite extension]] of the [[p-adic number|''p''-adic numbers]] '''Q'''_''p'', and if ''v_p'' denotes the [[p-adic va ...

...pecifically it tells us that we can get a good approximation to irrational numbers that are not quadratic by using either [[quadratic irrational]]s or simply ...l zero, the first non-zero one among them is positive, they are relatively prime, and we have ...

...ic]] [[univalent function]]s defined on the [[unit disk]] in the [[complex numbers]]. The theorem states that a univalent function defined on the unit disc, ...e]] with respect to 0, , i.e. it is invariant under multiplication by real numbers in (0,1). ...