منابع مشابه
Perfect Numbers with Identical Digits
Suppose g ≥ 2. A natural number N is called a repdigit in base g if it has the shape a g −1 g−1 for some 1 ≤ a < g, i.e., if all of its digits in its base g expansion are equal. The number N is called perfect if σ(N) = 2N , where σ(N) := � d|N d is the usual sum of divisors function. We show that in each base g, there are at most finitely many repdigit perfect numbers, and the set of all such n...
متن کاملOn Binary Representations of Integers with Digits
Güntzer and Paul introduced a number system with base 2 and digits −1, 0, 1 which is characterized by separating nonzero digits by at least one zero. We find an explicit formula that produces the digits of the expansion of an integer n which leads us to many generalized situations. Syntactical properties of such representations are also discussed. 1. A binary number system Integers n can be wri...
متن کاملApproximate Polynomial GCD over Integers with Digits-wise Lattice
For the given coprime polynomials over integers, we change their coefficients slightly over integers so that they have a greatest common divisor (GCD) over integers. That is an approximate polynomial GCD over integers. There are only two algorithms known for this problem. One is based on an algorithm for approximate integer GCDs. The other is based on the well-known subresultant mapping and the...
متن کاملOn the Sum of Digits of Some Sequences of Integers
Let b ≥ 2 be a fixed positive integer. We show for a wide variety of sequences {an}n=1 that for most n the sum of the digits of an in base b is at least cb log n, where cb is a constant depending on b and on the sequence. Our approach covers several integer sequences arising from number theory and combinatorics.
متن کامل#A3 INTEGERS 12A (2012): John Selfridge Memorial Issue PERFECT POWERS WITH FEW TERNARY DIGITS
We classify all integer squares (and, more generally, q-th powers for certain values of q) whose ternary expansions contain at most three digits. Our results follow from Padé approximants to the binomial function, considered 3-adically. –Dedicated to the memory of John Selfridge.
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1989
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-53-2-187-205