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 principal office of history I take to be this: to prevent virtuous actions from being forgotten, and that evil words and deeds should fear an infamous reputation with posterity.”
—Tacitus (c. 55–c. 120)
“If the alternative is to keep all just men in prison, or give up war and slavery, the State will not hesitate which to choose.”
—Henry David Thoreau (1817–1862)
“Is it true or false that Belfast is north of London? That the galaxy is the shape of a fried egg? That Beethoven was a drunkard? That Wellington won the battle of Waterloo? There are various degrees and dimensions of success in making statements: the statements fit the facts always more or less loosely, in different ways on different occasions for different intents and purposes.”
—J.L. (John Langshaw)