History and Alternative Statements
There are a number of ways to state the theorem. Keep in mind that Euler and Legendre did not have Gauss's congruence notation, nor did Gauss have the Legendre symbol.
In this article p and q always refer to distinct positive odd primes.
Read more about this topic: Quadratic Reciprocity
Famous quotes containing the words history, alternative and/or statements:
“The foregoing generations beheld God and nature face to face; we, through their eyes. Why should not we also enjoy an original relation to the universe? Why should not we have a poetry and philosophy of insight and not of tradition, and a religion by revelation to us, and not the history of theirs?”
—Ralph Waldo Emerson (1803–1882)
“It is a secret from nobody that the famous random event is most likely to arise from those parts of the world where the old adage “There is no alternative to victory” retains a high degree of plausibility.”
—Hannah Arendt (1906–1975)
“Science is a system of statements based on direct experience, and controlled by experimental verification. Verification in science is not, however, of single statements but of the entire system or a sub-system of such statements.”
—Rudolf Carnap (1891–1970)