Sum of two squares theorem
In number theory, the sum of two squares theorem says when an integer can be written as a sum of two squares, that is when for some integers .
- An integer greater than one can be written as a sum of two squares if and only if in its prime decomposition there is no prime congruent to 3 (mod 4) raised to an odd power.[1]
This theorem supplements Fermat's two-square theorem which says when a prime number can be written as a sum of two squares, in that it also covers the case for composite numbers.
See also
- Brahmagupta–Fibonacci identity. This identity entails that the set of all sums of two squares is closed under multiplication.
- Landau–Ramanujan constant, used in a formula for the density of the numbers that are sums of two squares
References
- ↑ Underwood Dudley (1978). Elementary Number Theory (2 ed.). W.H. Freeman and Company.
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