(m^2-n^2)^2+(2mn)^2=(m^2+n^2)^2
より,
a=α^2+2αβ=m^2-n^2
b=2β^2+2αβ=2mn
c=α^2+2αβ+2β^2=m^2+n^2
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2m^2=2α^2+4αβ+2β^2=2(α+β)^2
2n^2=2β^2
m=α+β,n=β