Abstract
In Chapter10 we discussed Diophantine equations over finitefields. In this chapter we consider special Diophantine equations with integral coefficients and seek integral or rational solutions. The techniques used vary from elementary congruence considerations to the use of more sophisticated results in algebraic number theory. In addition to establishing the existence or nonexistence of solutions we also obtain results of a quantitative nature, as in the determination of the number of representations of an integer as the sum of four squares. All of the equations considered in this chapter are classical, each playing an important role in the historical development of the subject.
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© 1990 Springer Science+Business Media New York
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Ireland, K., Rosen, M. (1990). Diophantine Equations. In: A Classical Introduction to Modern Number Theory. Graduate Texts in Mathematics, vol 84. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-2103-4_17
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DOI: https://doi.org/10.1007/978-1-4757-2103-4_17
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Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-3094-1
Online ISBN: 978-1-4757-2103-4
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