On the diophantine equation \(x^{10}{\pm{}}y^{10}=z^ 2\). (English) Zbl 0779.11018
A new elementary proof, mainly based on congruences, is given to show that the equations \(x^{10} \pm y^{10} = z^ 2\) in integers \(x\), \(y\) and \(z\) have no nontrivial solutions.
Reviewer: B.Brindza (Debrecen)
MSC:
| 11D41 | Higher degree equations; Fermat’s equation |
Keywords:
diophantine equations of degree tenReferences:
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