Fermat 4n+1 Theorem

Every Prime of the form $4n+1$ is a sum of two Square Numbers in one unique way (up to the order of Summands). The theorem was stated by Fermat , but the first published proof was by Euler.

See also Sierpinski's Prime Sequence Theorem, Square Number

References

Hardy, G. H. and Wright, E. M. ``Some Notation.'' Th. 251 in An Introduction to the Theory of Numbers, 5th ed. Oxford, England: Clarendon Press, 1979.