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Sum of two squares theorem
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Sum of two squares theorem : ウィキペディア英語版
Sum of two squares theorem
In number theory, the sum of two squares theorem says when an integer n>1 can be written as a sum of two squares, that is when n=a^2 + b^2 for some integers a, b.
:''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.''
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.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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