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The Diophantine equation x^4 +- y^4 = iz^2 in Gaussian integers (CROSBI ID 156968)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Najman, Filip
The Diophantine equation x^4 +- y^4 = iz^2 in Gaussian integers // American mathematical monthly, 117 (2010), 5; 637-641. doi: 10.4169/000298910X496769
Podaci o odgovornosti
Najman, Filip
engleski
The Diophantine equation x^4 +- y^4 = iz^2 in Gaussian integers
In this note we find all the solutions of the Diophantine equation x^4 +- y^4 = iz^2 using elliptic curves over Q(i). Also, using the same method we give a new proof of Hilbert's result that the equation x^4 +- y^4 = z^2 has only trivial solutions in Gaussian integers.
Fermat equation ; Gaussian integers
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Podaci o izdanju
117 (5)
2010.
637-641
objavljeno
0002-9890
1930-0972
10.4169/000298910X496769
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