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...uisenaire rods 6.png|thumb|Demonstration, with [[Cuisenaire rods]], of the arithmetic nature of the number 6]] ...number|positive]] [[divisor]]s is also an integer. For instance, 6 is an arithmetic number because the average of its divisors is ...

...issue=1|year=2014|pages=58–76|title=On a conjecture of Rudin on squares in arithmetic progressions|author=González-Jiménez, Enrique|author2=Xarles, Xavier|doi=10 ...q, a)</math> to be the number of [[square number|perfect square]]s in the arithmetic progression <math>qn + a</math>, for <math>n = 0, 1, \ldots, N-1</math>, an ...

{{Short description|Set of all true first-order statements about the arithmetic of natural numbers}} ...e set of all true [[first-order logic|first-order]] statements about the [[arithmetic]] of [[natural number]]s.<ref>{{Harvnb|Boolos|Burgess|Jeffrey|2002|p=295}}< ...

In the study of the arithmetic of [[elliptic curves]], the '''''j''-line''' over a [[ring (mathematics)|ri | series = Annals of Mathematics Studies ...

In [[number theory]], a '''normal order of an arithmetic function''' is some simpler or better-understood function which "usually" t * [[Average order of an arithmetic function]] ...

{{Short description|System of arithmetic in proof theory}} {{redirect|Elementary recursive arithmetic|the computational complexity class|Elementary recursive function}} ...

...he [[prime ideal spectrum]] Spec(''Z'') being seen as analogous to a line. Arithmetic surfaces arise naturally in [[diophantine geometry]], when an [[algebraic c In more detail, an arithmetic surface <math>S</math> (over the Dedekind domain <math>R</math>) is a [[S ...

...\to a</math>.<ref name="Knopp">[[Konrad Knopp]]: ''Infinite Sequences and Series''. Dover, 1956, pp. 33-36</ref><ref name="Heuser">[[Harro Heuser]]: ''Lehrb If the arithmetic means in Cauchy's limit theorem are replaced by [[weighted arithmetic mean]]s those converge as well. More precisely for sequence <math> (a_n)</m ...

== Interpretability of arithmetic == ...red Tarski|Tarski]] and [[Wanda Szmielew|Szmielew]] showed that [[Robinson arithmetic]] (<math>{\mathsf{Q}}</math>) can be interpreted in a weak set theory whose ...

...cription|Theorem in probabilistic number theory on additive complex-valued arithmetic functions}} ...babilistic Number Theory |publisher=Cambridge University Press |volume=46 |series=Cambridge studies in advanced mathematics |isbn=0-521-41261-7}}</ref>{{Rp|3 ...

...e arithmetic billiard for the numbers 15 and 40.|right|thumb|500x500px|The arithmetic billiard for the numbers 15 and 40: the greatest common divisor is 5, the l In recreational [[mathematics]], '''arithmetic billiards''' provide a geometrical method to determine the [[least common m ...

...he [[function composition|composition]] of a finite number of [[arithmetic|arithmetic operations]] {{nowrap|(+, −, ×, ÷)}}, [[exponential function|exponential]]s ...erentiation]]. It is not closed under [[Limit of a sequence|limits]] and [[series (mathematics)|infinite sums]]. {{example needed|date=December 2020}} ...

...://www.sciencedirect.com/science/article/pii/0003484374900011 Second-order Arithmetic and Some Related Topics]" (1973), p. 181</ref><ref>J.-Y. Girard, ''Proof Th ...oclc=288374692}}</ref>^p.&nbsp;243 Every β-model of second-order arithmetic is also an ω-model, since working within the model we can prove that &lt; i ...

...tate the relationship between the [[harmonic mean]], [[geometric mean]], [[arithmetic mean]], and [[Root mean square|quadratic mean]] (also known as root mean sq ...inger |others=International mathematical olympiad |isbn=978-1-4419-9854-5 |series=Problem books in mathematics |location=New York |pages=7}}</ref> ...

...eep. The first block is a unit block and the dashed line represents the [[#Series|infinite sum]] of the sequence, a number that it will forever approach but The sum of a geometric progression's terms is called a ''[[geometric series]]''. ...

* [[Arithmetic derivative]] ...ferential Equations|year=1989|publisher=Springer-Verlag|isbn=0-8218-3862-8|series=Mathematical Surveys and Monographs}}. ...

{{distinguish|Arithmetic–geometric mean}} {{Calculus |Series}} ...

In the mathematical fields of [[algebraic geometry]] and [[arithmetic geometry]], the '''Consani–Scholten quintic''' is an [[algebraic variety|al ...Scholten constructed a [[Hilbert modular form]] and conjectured that its L-series agreed with the Galois representations for their curve; this was proven by ...

...publisher=[[Springer-Verlag]] | location=Berlin, New York | edition=2nd | series=Graduate Texts in Mathematics | isbn=978-0-387-96508-6 |mr=890960 | year=19 [[Category:Modular arithmetic]] ...

{{Short description|Progression formed by taking the reciprocals of an arithmetic progression}} ...|reciprocals]] of an [[arithmetic progression]], which is also known as an arithmetic sequence. ...