Category:Law of Quadratic Reciprocity
Jump to navigation
Jump to search
This category contains pages concerning Law of Quadratic Reciprocity:
Let $p$ and $q$ be distinct odd primes.
Then:
- $\paren {\dfrac p q} \paren {\dfrac q p} = \paren {-1}^{\dfrac {\paren {p - 1} \paren {q - 1} } 4}$
where $\paren {\dfrac p q}$ and $\paren {\dfrac q p}$ are defined as the Legendre symbol.
An alternative formulation is: $\paren {\dfrac p q} = \begin{cases} \quad \paren {\dfrac q p} & : p \equiv 1 \lor q \equiv 1 \pmod 4 \\ -\paren {\dfrac q p} & : p \equiv q \equiv 3 \pmod 4 \end{cases}$
The fact that these formulations are equivalent is immediate.
This fact is known as the Law of Quadratic Reciprocity, or LQR for short.
Pages in category "Law of Quadratic Reciprocity"
The following 13 pages are in this category, out of 13 total.
F
- First Supplement to Law of Quadratic Reciprocity
- First Supplement to Law of Quadratic Reciprocity/Examples
- First Supplement to Law of Quadratic Reciprocity/Examples/11
- First Supplement to Law of Quadratic Reciprocity/Examples/13
- First Supplement to Law of Quadratic Reciprocity/Examples/17
- First Supplement to Law of Quadratic Reciprocity/Examples/19
- First Supplement to Law of Quadratic Reciprocity/Examples/3
- First Supplement to Law of Quadratic Reciprocity/Examples/5
- First Supplement to Law of Quadratic Reciprocity/Examples/7