منابع مشابه
Perfect repdigits
Here, we give an algorithm to detect all perfect repdigits in any base g > 1. As an application, we find all such examples when g ∈ [2, . . . , 333], extending a calculation from [2]. In particular, we demonstrate that there are no odd perfect repdigits for this range of bases. [2010]Primary 11A63, 11A05, 11A25
متن کاملOdd Repdigits to Small Bases Are Not Perfect
We demonstrate, by considering each base in the range 2 through 9, that no odd repdigit with a base in that range is a perfect number.
متن کاملAliquot Cycles of Repdigits
Here we show that the only aliquot cycle consisting only of rep-digits in base 10 is the cycle consisting of the perfect number 6. Generally, we show that if g is an even positive integer, then there are only finitely many aliquot cycles consisting entirely of repdigits in base g, which are, at least in principle, effectively computable.
متن کاملRepdigits as sums of three Fibonacci numbers
In this paper, we find all base 10 repdigits which are sums of three Fibonacci numbers. AMS subject classifications: Primary 11D61; Secondary 11A67, 11B39
متن کاملAn Explicit Bound for Aliquot Cycles of Repdigits
We find an explicit bound, in terms of g when it is even, for the largest element of an aliquot cycle of repdigits to base g.
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2013
ISSN: 0025-5718,1088-6842
DOI: 10.1090/s0025-5718-2013-02682-8