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:
“We said that the history of mankind depicts man; in the same way one can maintain that the history of science is science itself.”
—Johann Wolfgang Von Goethe (17491832)
“If you have abandoned one faith, do not abandon all faith. There is always an alternative to the faith we lose. Or is it the same faith under another mask?”
—Graham Greene (19041991)
“He admired the terrible recreative power of his memory. It was only with the weakening of this generator whose fecundity diminishes with age that he could hope for his torture to be appeased. But it appeared that the power to make him suffer of one of Odettes statements seemed exhausted, then one of these statements on which Swanns spirit had until then not dwelled, an almost new word relayed the others and struck him with new vigor.”
—Marcel Proust (18711922)