Note on the Inequality Theorem that mx m–1( x – 1)> xm – 1> m( x – 1) unless when 0< m<1, when mx m–1( x – 1)< xm – 1< m( x – 1), where x is any positive quantity other than unity
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There is no restriction in assuming that y > x in (1) and thus we have m > n. This equation asks for integers having all their digits equal to one with respect to two distinct bases and we still do not know whether or not it has finitely many solutions. Even if we fix one of the four variables, it remains an open question to prove that (1) has finitely many solutions. However, when either the b...
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ژورنال
عنوان ژورنال: Proceedings of the Edinburgh Mathematical Society
سال: 1901
ISSN: 0013-0915,1464-3839
DOI: 10.1017/s001309150003279x