Did Euler Know Quadratic Reciprocity?: New Insights from a Forgotten Work - References

References

[1] Calinger, R. Leonhard Euler: Life and Thought, in Leonhard Euler: Life, Work, and Legacy (Bradley and Sandifer, eds.), pp. 5–60. Washington, DC: MAA, 2007.

[2] Dickson, L. History of the Theory of Numbers, 3 vols. New York: Chelsea Publishing Company, 1919, 1920, 1923.

[3] Edwards, H. M. Euler and Quadratic Reciprocity.  Math. Mag. 56(3), pp. 285–291, 1983.

[4] Euler, L. Theoremata circa divisores numerorum in hac forma \(paa \pm qbb\) contentorum} (E164).  Commentarii academiae scientiarum Petropolitanae 14 (1751), pp. 151–181.  Reprinted in Opera Omnia: Series 1, Volume 2, pp. 194–222.  Original article available online, along with an English translation by Jordan Bell, at eulerarchive.maa.org. 

[5] Euler, L. Demonstratio theorematis Fermatiani omnem numerum primum formae \(4n+1\) esse summam duorum quadratorum (E241).  Novi Commentarii academiae scientiarum Petropolitanae 5 (1760), pp. 3–13.  Reprinted in Opera Omnia: Series 1, Volume 2, pp. 328–337.  Original article available online, along with an English translation by Mark Snavely and Phil Woodruff, at eulerarchive.maa.org.

[6] Euler, L. Specimen de usu observationum in mathesi pura (E256).  Novi Commentarii academiae scientiarum Petropolitanae 6 (1761), pp. 185–230.  Reprinted in Opera Omnia: Series 1, Volume 2, pp. 459–492.  Original article available online at eulerarchive.maa.org.

[7] Euler, L. De divisoribus numerorum in forma \(mxx + nyy\) contentorum (E744).  Mémoires de l'académie des sciences de St.-Pétersbourg 5 (1815), pp. 3–23.  Reprinted in Opera Omnia: Series 1, Volume 4, pp. 418–431.  Original article online at eulerarchive.maa.org.

[8] Fuss, P. Correspondance mathématique et physique de quelques célèbres géomètres du XVIIIème siècle, Saint Petersbourg, 1845.

[9] Fenster, D. D. Why Dickson Left Quadratic Reciprocity out of His History of the Theory of Numbers.  Am. Math. Month. 106(7), pp. 618–627, 1999.

[10] de Fermat, P.  Œuvres.  Gauthier-Villars, Paris, 1891–1896.

[11] Gauss, C.  Disquisitiones Arithmeticae, 1801.

[12] Grattan-Guiness, I. The Mathematics of the Past: Distinguishing its history from our heritage.  Historia Mathematica 31(2), pp. 163–185, 2004.

[13] Legendre, A. M.  Essai sur la Théorie des Nombres.  Paris, 1798.

[14] Lemmermeyer, F.  Reciprocity Laws: from Euler to Eisenstein.  Springer, 2000.

[15] Sandifer, E.  Factors of Forms.  Contained in collection How Euler Did It, pp. 67–74.  Washington, DC: MAA, 2007.  Original article also available online at eulerarchive.maa.org.

[16] Truesdell, C.  An Idiot's Fugitive Essays on Science.  Springer, 1984.

[17] Yandell, B.  The Honors Class: Hilbert's Problems and Their Solvers.  AK Peters, 2001.