Catalan's equation has no new solution with either exponent less than 10651.
Mignotte, Maurice, Roy, Yves (1995)
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Mignotte, Maurice, Roy, Yves (1995)
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Andreas Čap (1990)
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Izhboldin, Oleg T. (1998)
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Hoffmann, Detlev W. (1996)
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We prove convergence results for `increasing' sequences of sectorial forms. We treat both the case of closed forms and the case of non-closable forms.
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The main goal of the paper is to examine the dimension of the vector space spanned by powers of linear forms. We also find a lower bound for the number of summands in the presentation of zero form as a sum of d-th powers of linear forms.