منابع مشابه
Odd Perfect numbers
It is not known whether or not odd perfect numbers can exist. However it is known that there is no such number below 10, (see Brent [1]). Moreover it has been proved by Hagis [4] and Chein [2] independently that an odd perfect number must have at least 8 prime factors. In fact results of this latter type can in principle be obtained solely by calculation, in view of the result of Pomerance [6] ...
متن کاملGuessing Numbers of Odd Cycles
For a given number of colours, s, the guessing number of a graph is the base s logarithm of the size of the largest family of colourings of the vertex set of the graph such that the colour of each vertex can be determined from the colours of the vertices in its neighbourhood. An upper bound for the guessing number of the n-vertex cycle graph Cn is n/2. It is known that the guessing number equal...
متن کاملHuygens' odd Sympathy Experiment Revisited
We repeat Huygens’ experiment using real pendulum clocks in the same way as it was done originally, i.e., we hang two clocks on the same beam and observe the behavior of the pendulums. The clocks in the experiment have been selected in such a way to be as identical as possible. It has been observed that when the beam is allowed to move horizontally, the clocks can synchronize both in-phase and ...
متن کاملOdd harmonic numbers exceed 1024
A number n > 1 is harmonic if σ(n) | nτ(n), where τ(n) and σ(n) are the number of positive divisors of n and their sum, respectively. It is known that there are no odd harmonic numbers up to 1015. We show here that, for any odd number n > 106, τ(n) ≤ n1/3. It follows readily that if n is odd and harmonic, then n > p3a/2 for any prime power divisor pa of n, and we have used this in showing that ...
متن کاملLinear Integer Arithmetic Revisited
We consider feasibility of linear integer programs in the context of verification systems such as SMT solvers or theorem provers. Although satisfiability of linear integer programs is decidable, many stateof-the-art solvers neglect termination in favor of efficiency. It is challenging to design a solver that is both terminating and practically efficient. Recent work by Jovanović and de Moura co...
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ژورنال
عنوان ژورنال: The American Mathematical Monthly
سال: 1942
ISSN: 0002-9890
DOI: 10.2307/2303780