Abstract
This question is as old as number theory, and its solution is a classic in the field. The “hard” part of the solution is to see that every prime number of the form 4m + 1 is a sum of two squares. G. H. Hardy writes that this two square theorem of Fermat “is ranked, very justly, as one of the finest in arithmetic.” Nevertheless, one of our Book Proofs below is quite recent.
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© 2018 Springer-Verlag GmbH Germany, part of Springer Nature
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Aigner, M., Ziegler, G.M. (2018). Representing numbers as sums of two squares. In: Proofs from THE BOOK. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-57265-8_4
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DOI: https://doi.org/10.1007/978-3-662-57265-8_4
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-57264-1
Online ISBN: 978-3-662-57265-8
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