An Introduction to Gausss Number Theory

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Contents

  1. Carl Friedrich Gauss
  2. Timeline of Mathematics
  3. Gauss and the prime number theorem
  4. Introduction to Number Theory
  5. Carl Friedrich Gauss

If there are an even number of least positive residues mod of these numbers , then is a quadratic residue of.

1. Introduction

If is odd , is a quadratic nonresidue. Gauss's lemma can therefore be stated as , where is the Legendre symbol. It was proved by Gauss as a step along the way to the quadratic reciprocity theorem Nagell Euclid's lemma states that for any two integers and , suppose.

Then if is relatively prime to , then divides. Encyclopaedia Britannica. II, p. I, pp.

Carl Friedrich Gauss

Euler was generous in giving credit to others Varadarajan , p. Early signs of self-consciousness are present already in letters by Fermat: thus his remarks on what number theory is, and how "Diophantus's work [ In Felix E. Browder ed. Mathematical Developments Arising from Hilbert Problems. Proceedings of Symposia in Pure Mathematics. American Mathematical Society. Andrews, American Mathematical Soc. Retrieved Apostol, Tom M. Introduction to analytic number theory.

Undergraduate Texts in Mathematics. Mathematical Reviews MathSciNet. Abteilung B:Studien in German.


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A History of Mathematics 2nd ed. New York: Wiley. University of Chicago Press. Colebrooke, Henry Thomas London: J. Davenport, Harold ; Montgomery, Hugh L. Multiplicative Number Theory. Graduate texts in mathematics. Edwards, Harold M. November Mathematics Magazine.

Graduate Texts in Mathematics. Springer Verlag. Fermat, Pierre de Varia Opera Mathematica in French and Latin. Toulouse: Joannis Pech.


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Historia Mathematica. In Christianidis, J. Classics in the History of Greek Mathematics. Berlin: Kluwer Springer. Disquisitiones Arithmeticae. Goldfeld, Dorian M. Goldstein, Catherine ; Schappacher, Norbert In Goldstein, C. The Shaping of Arithmetic after C. Gauss's "Disquisitiones Arithmeticae". Granville, Andrew The Princeton Companion to Mathematics. Princeton University Press. Porphyry ; Guthrie, K. Life of Pythagoras.

Alpine, New Jersey: Platonist Press. Guthrie, Kenneth Sylvan The Pythagorean Sourcebook and Library. Grand Rapids, Michigan: Phanes Press. Hardy, Godfrey Harold ; Wright, E. An Introduction to the Theory of Numbers Sixth ed. Oxford University Press. Heath, Thomas L. Oxford: Clarendon Press.

Timeline of Mathematics

Hopkins, J. In Young, M. Religion, Learning and Science in the 'Abbasid Period. The Cambridge history of Arabic literature. Cambridge University Press.

Gauss and the prime number theorem

Huffman, Carl A. Zalta, Edward N. Stanford Encyclopaedia of Philosophy Fall ed. Retrieved 7 February Iwaniec, Henryk ; Kowalski, Emmanuel Analytic Number Theory.

Introduction to Number Theory

American Mathematical Society Colloquium Publications. Plato ; Jowett, Benjamin trans. Singapore: World Scientific. Long, Calvin T. Elementary Introduction to Number Theory 2nd ed. Lexington, VA: D. Heath and Company. Mahoney, M. Milne, J. Available at www.

Carl Friedrich Gauss

Morrow, Glenn Raymond trans. A Commentary on Book 1 of Euclid's Elements.


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