# Representing numbers as sums of two squares

• Martin Aigner
• Günter M. Ziegler

## 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.

## Keywords

Equivalence Class Prime Factor Prime Number Euclidean Algorithm Prime Number Theorem
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## References

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