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$${Published}$$  $${Online}$$  $${First}$$  $${(21/1/2024)}$$
$${Latest}$$  $${corrections}$$  $${(24/1/2024)}$$
$${Latest}$$  $${additions}$$  $${(29/1/2024)}$$
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$${Diophantine}$$ $${equation}$$ $${1}$$
$${(1.1)}$$  $${Pythagorean}$$ $${triple}$$
$${(1)}$$  $${x^2+y^p=z^2}$$    $${(p=2,3,p≧4)}$$
$${(1.1)}$$  $${x^2+y^2=z^2}$$  $${(p=2)}$$
$${(1.2)}$$  $${x^2+y^3=z^2}$$  $${(p=3)}$$
$${(1.3)}$$  $${x^2+y^p=z^2}$$  $${(p≧4)}$$
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$${Diophantine}$$ $${equation}$$ $${2}$$
$${(2)}$$  $${x^2+ky^p=z^2}$$    $${(p=2,p≧3)}$$
$${(2.1)}$$  $${x^2+ky^2=z^2}$$  $${(p=2)}$$
$${(2.2)}$$  $${x^2+ky^p=z^2}$$  $${(p≧3)}$$
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$${Diophantine}$$ $${equation}$$ $${3}$$
$${(3)}$$  $${x^2+y^2=z^{2^k}}$$    $${(k=2,k≧3)}$$
$${(3.1)}$$  $${x^2+y^2=z^4}$$  $${(k=2)}$$
$${(3.2)}$$  $${x^2+y^2=z^8}$$  $${(k=3)}$$
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$${Diophantine}$$ $${equation}$$ $${4}$$
$${(4)}$$  $${x^2+y^2=2z^{2^k}}$$    $${(k=1,2,k≧3)}$$
$${(4.1)}$$  $${x^2+y^2=2z^2}$$  $${(k=1)}$$
$${(4.2)}$$  $${x^2+y^2=2z^4}$$  $${(k=2)}$$
$${(4.3)}$$  $${x^2+y^2=2z^{2^k}}$$  $${(k≧3)}$$
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$${Diophantine}$$ $${equation}$$ $${5}$$
$${(5.1)}$$  $${x^2+y^2=z^2+w^2}$$
$${(5.2)}$$  $${x^2+y^2=z^2+w^4}$$
$${(5.3)}$$  $${x^2+y^2=z^2+w^{4p}}$$
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$${Diophantine}$$ $${equation}$$ $${6}$$
$${(6.1)}$$  $${x^2+y^2=z^2+w^3}$$
$${(6.2)}$$  $${x^2+y^6=z^2+w^3}$$
$${(6.3)}$$  $${x^2+y^6=z^2+w^{3p}}$$
$${(6.4)}$$  $${x^2+y^{6p}=z^2+w^{3p}}$$
$${(6.5)}$$  $${x^{34}+y^{18}=z^2+w^9}$$(おまけ)
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$${Diophantine}$$ $${equation}$$ $${7}$$
$${(7.1)}$$  $${x^2+y^2=z^2+w^p}$$
$${(7.2)}$$  $${x^2+y^{2p}=z^2+w^p}$$
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$${Diophantine}$$ $${equation}$$ $${8}$$
$${(8.1)}$$  $${x^2+y^2+z^2=w^2}$$
$${(8.2)}$$  $${x^2+y^2+z^2=w^4}$$
$${(8.3)}$$  $${x^2+y^{4k}+z^2=w^2}$$  $${(k=1)}$$
$${(8.4)}$$  $${x^2+y^{4k}+z^2=w^2}$$  $${(k≧2)}$$
$${(8.5)}$$  $${x^2+y^4+z^2=w^4}$$
$${(8.6)}$$  $${x^2+y^4+z^4=w^2}$$
$${(8.7)}$$  $${x^{14}+y^8+z^4=w^2}$$(おまけ)
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$${Diophantine}$$ $${equation}$$ $${9}$$
$${(9.1)}$$  $${4x^4+y^4+z^4=w^4}$$
$${(9.2)}$$  $${x^4+2y^4+2z^4=w^4}$$
$${(9.3)}$$  $${x^4+y^4+2z^2=w^4}$$
$${(9.4)}$$  $${x^6+y^6+3z^2=w^6}$$
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$${Diophantine}$$ $${equation}$$ $${10}$$
$${(10.1)}$$  $${x^3+y^3+3z^2=w^3}$$
$${(10.2)}$$  $${x^3+y^3+z^2=w^3}$$
$${(10.3)}$$  $${x^7+y^7+7z^2=w^7}$$
$${(10.4)}$$  $${x^{14}+y^{28}+7z^2=w^{14}}$$(おまけ)
$${(10.5)}$$  $${x^7+y^7+z^2=w^7}$$
$${(10.6)}$$  $${x^{14}+y^7+z^2=w^{14}}$$(おまけ)
$${(10.7)}$$  $${x^{14}+y^7+z^2=w^{56}}$$(おまけ)
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$${etc}$$  目次[002]・【003】
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