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The point was that the sum of two squares theorem gives a stronger property than just ≢ 3 mod 4. But ok, let's inline the statement here. |
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A Gaussian integer {{math|''a'' + ''bi''}} is a Gaussian prime if and only if either:
*one of {{math|''a'', ''b''}} is zero and the [[absolute value]] of the other is a prime number of the form {{math|4''n'' + 3}} (with {{mvar|n}} a nonnegative integer), or
*both are nonzero and {{math|''a''<sup>2</sup> + ''b''<sup>2</sup>}} is a prime number (which will ''
In other words, a Gaussian integer {{math|''m''}} is a Gaussian prime if and only if either its norm is a prime number, or {{math|''m''}} is the product of a unit ({{math|±1, ±''i''}}) and a prime number of the form {{math|4''n'' + 3}}.
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