A one-sentence proof that every prime p \\equiv 1\\pmod 4 is a sum of two 
squares.

Zagier, Don

doi:10.2307/2323918

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学術論文

A one-sentence proof that every prime p \\equiv 1\\pmod 4 is a sum of two squares.

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Zagier, Don
Max Planck Institute for Mathematics, Max Planck Society;

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引用

Zagier, D. (1990). A one-sentence proof that every prime p \\equiv 1\\pmod 4 is a sum of two squares. American Mathematical Monthly, 97(2), 144. doi:10.2307/2323918.

引用: https://hdl.handle.net/21.11116/0000-0004-3932-4

要旨

The one sentence defines an involution, on the set S=(x,y,z)\\in \\Bbb N\\sp 3 : x\\sp 2+4yz=p, whose fixed point gives a representation of p as the sum of squares (but only implicitly).\\par [See the following review.].