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Essay / Research Paper Abstract
This 8 page paper examines the way in which Gauss added to number theory, looking specifically congruence and quadratic reciprocity the paper shows how and why this was the start of modern number theory. The law of quadratic reciprocity is also explained with the use of examples. The paper then goes on to look at how Gauss’s work can be seen as useful today with example of forecasting with the use of the ordinary least squares mouthed (OLS). The bibliography cites 8 sources.
Page Count:
8 pages (~225 words per page)
File: TS14_TEgauss.rtf
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Unformatted sample text from the term paper:
the properties of numbers, particularly integers and the wider range of issues that arise with their study. Number theory can also be sub divided into many different areas according to
the type of problem under investigations and the way the investigation is taking place. The beginning of modern number theory is seen in the eighteenth century with theorists such
as Legendre and Gauss and the publication and the publication of Gausss Disquisitiones Arithmeticae in 1801 (Dedekind, 1983, Hardy and Wright, 1980). Disquisitiones Arithmeticae was one of the most important
publications in terms of number theory and the way in which integers are dealt with. Gauss saw this as the most important area of aromatic. Stating that "Mathematics is the
queen of the sciences and number theory is the queen of mathematics" (Bell, 1986). Gausss area of study was mainly with congruent numbers, these are numbers where there will
be the same reminder when they are divided by another number, (Dedekind, 1983). For example, 7 and 9 are both congruent to
the number 2, phased as modulo 2, as when they are divided by 2 they will both have a reminder or 1. It was this that gave rise to the
first conclusive proof of quadratic reciprocity and the quadratic residues. a is called quadratic residue with respect to b, if there is an integer x such that when a is
divided by b, the remainder is the same as x2 divided by b (Hardy and Wright, 1980). This was an approach that brought together a number of different areas of
study, including geometric ideas as well as algebra and arithmetic (Bell, 1986) One example of the use of this was the way that
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