Abstract
Abstract By universal agreement C. F. Gauss (1777-1855) was a mathematical genius of the highest order, to be considered alongside such giants as Newton and Einstein. He made many discoveries both inside and outside mathematics, but in his time he was probably best known as an astronomer—he was director of the Gottingen Observatory for many years. Number theory was one of his great passions he called it the ·Queen of Mathematics·. In 1801, at the age of 24. he published one of the classics of mathematical literature. Disquisitiones Arithmeticae, which contained a wealth of new ideas and theorems and which laid the foundation for modern number theory. A translation has been published (Gauss 1966) and the reader should try to study it. Many of the results presented below first appeared in Gauss’s classic, particularly those concerning quadratic reciprocity, primitive roots. and quadratic form theory.
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