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There is a very slick proof (discussed herehere on MO) that every prime $p=4k+1$ is a sum of two squares, which looks at the set $S= \{(x,y,z) \in N^3: x^2+4yz=p \}$ and shows that a particular involution of $S$ has exactly one fixed point.
There is a very slick proof (discussed here on MO) that every prime $p=4k+1$ is a sum of two squares, which looks at the set $S= \{(x,y,z) \in N^3: x^2+4yz=p \}$ and shows that a particular involution of $S$ has exactly one fixed point.
There is a very slick proof (discussed here on MO) that every prime $p=4k+1$ is a sum of two squares, which looks at the set $S= \{(x,y,z) \in N^3: x^2+4yz=p \}$ and shows that a particular involution of $S$ has exactly one fixed point.
There is a very slick proof (discussed here on MO) that every prime $p=4k+1$ is a sum of two squares, which looks at the set $S= \{(x,y,z) \in N^3: x^2+4yz=p \}$ and shows that a particular involution of $S$ has exactly one fixed point.
