Title: Theory / Unimportant / Math / Number Theory / Hardy - Wright{ / 05 Modulo
Tags: fromMath mathToSee récupéré

Definition: \(m\) divides \((x-a)\)
Page: 58
Chapter: 5
Section: 2
Variables: \(x,a\) real
\(m\) integers
Notation: \(x\equiv a\mod m\)

Definition: \(x\not\equiv a\mod m\)
Page: 58
Chapter: 5
Section: 2
Variables: \(x,a\) real
\(m\) integers

Name: The least residue of \(x\) modulo \(m\)
Definition: a residue of x in \([0,m)\)
Page: 58
Chapter: 5
Section: 2
Variables: \(x\) real
\(m\) integers

Name: A residue of \(x\) modulo \(m\)
Definition: a number equivalent to \(x\) modulo \(m\)
Page: 58
Chapter: 5
Section: 2
Variables: \(x\) real
\(m\) integers

Smaller0: \(a\equiv b\mod m_1\) and \(a\equiv b\mod m_2\)
Greater0: \(a\equiv b\mod \{m_1,m_2\}\)
Page: 58
Chapter: 5
Section: 2
Variables: \(a,b\) reals
\(m_1,m_2\) integrals
Index: 53
Kind: Theo
Smaller to greater: iff

Smaller0: \(ka\equiv kb\mod m\)
Greater0: \(a\equiv b\mod \frac m{(m,k)}\)
Page: 61
Chapter: 5
Section: 2
Variables: \(a,b\) reals
\(m\) integrals
Index: 54
Kind: Theo

Smaller0: \(ka\equiv kb\mod m\)
Greater0: \(a\equiv b\mod m\)
Page: 61
Chapter: 5
Section: 2
Variables: \(a,b\) reals
\(m\) integrals
Index: 55
Kind: Theo
Smaller1: \((k,m)=1\)

Name: Complete system of incongruent residues mod \(m\)
Page: 61
Section: 2
Chapter: 5
Index: 56
Variables: \(m\) integer
Kind: Theo
Under: multiplication by a number coprime to \(m\)

Name: Congruence modulo \(m\)
Page: 60
Section: 2
Chapter: 5
Variables: \(m\) integer
Under: addition of a constant
Under2: multiplication of a constant
Under3: addition of another congruent pair
Under4: multiplication of another congruent pair
Not5: not
Under5: division
CounterExample5: \(2\equiv 6  \mod 4\) while \(1\not\equiv3\mod4\)
Under6: power by an integral constant

Smaller0: \(xk\equiv l\mod m\) has a solution
Greater0: \((k,m)\) divides \(l\)
Page: 62
Chapter: 5
Section: 2
Variables: \(k,l,m\) integers,
\(x\) an integral variable
Smaller to greater: iff
Smallest: the number of solutions of \(xk\equiv l\mod m\) is \((k,m)\)

Name: A multiplicative function
Definition: A function \(f\) such that \(f(xy)=f(x)f(y)\)
Page: 64
Chapter: 5
Kind: Theo