Lagrange’s Four-Square Theorem

Yasushige Watase

Formalized Mathematics (2014)

  • Volume: 22, Issue: 2, page 105-110
  • ISSN: 1426-2630

Abstract

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This article provides a formalized proof of the so-called “the four-square theorem”, namely any natural number can be expressed by a sum of four squares, which was proved by Lagrange in 1770. An informal proof of the theorem can be found in the number theory literature, e.g. in [14], [1] or [23]. This theorem is item #19 from the “Formalizing 100 Theorems” list maintained by Freek Wiedijk at http://www.cs.ru.nl/F.Wiedijk/100/.

How to cite

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Yasushige Watase. "Lagrange’s Four-Square Theorem." Formalized Mathematics 22.2 (2014): 105-110. <http://eudml.org/doc/268883>.

@article{YasushigeWatase2014,
abstract = {This article provides a formalized proof of the so-called “the four-square theorem”, namely any natural number can be expressed by a sum of four squares, which was proved by Lagrange in 1770. An informal proof of the theorem can be found in the number theory literature, e.g. in [14], [1] or [23]. This theorem is item #19 from the “Formalizing 100 Theorems” list maintained by Freek Wiedijk at http://www.cs.ru.nl/F.Wiedijk/100/.},
author = {Yasushige Watase},
journal = {Formalized Mathematics},
keywords = {Lagrange’s four-square theorem},
language = {eng},
number = {2},
pages = {105-110},
title = {Lagrange’s Four-Square Theorem},
url = {http://eudml.org/doc/268883},
volume = {22},
year = {2014},
}

TY - JOUR
AU - Yasushige Watase
TI - Lagrange’s Four-Square Theorem
JO - Formalized Mathematics
PY - 2014
VL - 22
IS - 2
SP - 105
EP - 110
AB - This article provides a formalized proof of the so-called “the four-square theorem”, namely any natural number can be expressed by a sum of four squares, which was proved by Lagrange in 1770. An informal proof of the theorem can be found in the number theory literature, e.g. in [14], [1] or [23]. This theorem is item #19 from the “Formalizing 100 Theorems” list maintained by Freek Wiedijk at http://www.cs.ru.nl/F.Wiedijk/100/.
LA - eng
KW - Lagrange’s four-square theorem
UR - http://eudml.org/doc/268883
ER -

References

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