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The three-square theorem of Gauss and Legendre

Published online by Cambridge University Press:  18 June 2020

Peter Shiu
Peter Shiu*
Affiliation:
353 Fulwood Road, Sheffield S10 3BQ, e-mail: p.shiu@yahoo.co.uk
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Extract

The following theorems are famous landmarks in the history of number theory.

Theorem 1 (Fermat-Euler): A number is representable as a sum of two squares if, and only if, it has the form PQ2, where P is free of prime divisors q ≡ 3 (mod 4).

Theorem 2 (Lagrange): Every number is representable as a sum of four squares.

Theorem 3 (Gauss-Legendre): A number is representable as a sum of three squares if, and only if, it is not of the form 4a (8n + 7).

Type
Articles
Information
The Mathematical Gazette , Volume 104 , Issue 560 , July 2020 , pp. 209 - 214
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Copyright
© Mathematical Association 2020

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References

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