Search results

...r a [[:wikt:plus|plus]] (+) sign in front. Zero usually has no sign.</ref> Integers can also be shown on a number line like this: ...eater than or smaller than any other integer. [[Consecutive integer]]s are integers that come after each other (as in <math>{1, 2, 3, 4}</math>). ...

...e=The Definitive Higher Math Guide to Long Division and Its Variants — for Integers|url=https://mathvault.ca/long-division/#Euclidean_Division_%E2%80%94_Termin ==The case of general integers == ...

...satisfies the [[congruence]] <math>b^{n-1}\equiv 1\pmod{n}</math> for all integers <math>b</math> which are [[coprime|relatively prime]] to <math>n</math>. Be ...ber]]s <math>p</math> satisfy <math>b^{p-1}\equiv 1\pmod{p}</math> for all integers <math>b</math> which are relatively prime to <math>p</math>. This has been ...

...n as <math>(\mathbb{Z}, \cdot)</math>. The name of the magma would be "The integers under multiplication". ...

where <math>a</math> and <math>b</math> are [[Integer|integers]]. ...

...re" real numbers than integers. This is often expressed by saying that the integers are ''[[Countable set|countable]]'' and that the real numbers are ''[[Uncou ...ems are inside the real numbers. For example, the [[rational number]]s and integers are all in the real numbers. There are also more complicated number systems ...

...an group because <math>(\mathbb{Z}, +)</math> is a group, and also for any integers <math>a</math> and <math>b</math>, the equation <math>a+b = b+a</math> is t ...

...cd(x, y)</math>, is the greatest (largest) number that divides both of the integers evenly.<ref>{{Cite web|date=2020-03-25|title=Comprehensive List of Algebra The GCD of any two positive integers can be defined as a [[recursive]] [[function (mathematics)|function]]: <mat ...

[[Category:Integers]] ...

...d three are greater than seven. This only makes sense because there are no integers between two and three. This kind of truth is called [[vacuous truth]]. ...

...ubling function φ(x) = 2x maps elements of '''Z''' to elements of the even integers '''2Z'''. Since φ(a+b) = 2(a+b) = 2a+2b = φ(a)+φ(b), adding in '''Z''' is s ...

...lso called '''clock arithmetic''', is a way of doing [[arithmetic]] with [[integers]]. Much like hours on a [[clock]], which repeat every twelve hours, once th ....wolfram.com|language=en}}</ref><ref>{{Cite web|date=2013-11-16|title=2.3: Integers Modulo n|url=https://math.libretexts.org/Bookshelves/Abstract_and_Geometric ...

In [[computer science]], -1 is a common initial value for integers. It is also used to show that a [[variable]] has no useful information. ...athematics)|ring]]. Ring is a concept of [[abstract algebra]] generalizing integers and real numbers. ...

...bsite=Math Vault|language=en-US}}</ref> Likewise, the LCM of more than two integers is the smallest positive integer that is divisible by each of them.<ref>{{C ...

# Any two consecutive integers are always '''coprime'''. ...

[[Category:Integers]] ...

...a [[positive number|positive]] [[integer]] ''n'' is the number of positive integers smaller than ''n'' which are [[coprime]] to ''n'' (they share no [[factor]] ...e it gives the size of the multiplicative [[Group_(mathematics)|group]] of integers [[modular arithmetic|modulo]] ''n''. More precisely, <math>\phi(n)</math> i ...

...example, for an equation over the rationals, one can find solutions in the integers. Then, the equation is a [[diophantine equation]]. One may also look for s ...

You can count the [[integers]] with <math>({0, 1, -1, 2, -2, 3, -3...})\,\!</math> Suppose the integers are counted differently, as ...