Quadratic reciprocity
| If p,q are odd primes, then |
( |
p
q |
)( |
q
p |
) |
= (-1)(p-1)/2(q-1)/2, where |
Another way of phrasing this, which is perhaps more useful, is that
| ( |
p
q |
) |
= |
( |
q
p |
) |
unless both p and q are
primes of the form 4k+3 |
Calculating the value of a Legendre symbol
Using the properties of the Legendre symbol . . . . . .
Internet references
Wikipedia: Law
of quadratic reciprocity
Numericana, Final Answers: Quadratic
Reciprocity
Related
pages in this website
| Jacobi
symbol — |
( |
a
n |
) |
, where a is any integer, and n
is a positive integer greater than 2, an extension of the Legendre
symbol. |
| Kronecker
symbol — |
( |
a
n |
) |
, where a and n are any integers,
an extension of the Jacobi symbol. |
Fermat's Little Theorem
Euler's Totient Theorem
|
