ecuacions diofàntiques enteres

x^{2}+y^{2}=z
[2k+1]^{2}+[(2i)·k]^{2}=[4k+1]


x^{2}+y^{2}=z^{2}
[3k]^{2}+[4k]^{2}=[5k]^{2}


x^{3}+y^{3}+z=s^{2}
[3k+1]^{3}+[3·e^{(pi/3)i}k]^{3}+[3k]=[9k^{2}+6k+1]=[3k+1]^{2}


x^{4}+( y^{2}+(-5)z^{2} )·[k]^{2}=[k]·s^{3}
[3k]^{4}+( [8k]^{2}+(-5)[2k]^{2} )·[k]^{2}=[125k^{4}]=[k]·[5k]^{3}


x^{4}+y^{4}+(-2)z^{2}+3=4s^{3}
[3k+1]^{4}+[3e^{(pi/4)i}k]^{4}+(-2)[3k]^{2}+3=4[27k^{3}+9k^{2}+3k+1]=4[3k+1]^{3}