Integers with dense divisors
نویسندگان
چکیده
منابع مشابه
Consecutive Integers with Equally Many Principal Divisors
Classifying the positive integers as primes, composites, and the unit, is so familiar that it seems inevitable. However, other classifications can bring interesting relationships to our attention. In that spirit, let us classify positive integers by the number of principal divisors they possess, where we define a principal divisor of a positive integer n to be any prime-power divisor pa|n which...
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Let S denote a set of positive integers and τ : S → be defined so that τ(s) is a proper divisor of s (that is, τ(s) divides s and τ (s) < s). The ensemble (S, τ ) is said to have the ‘distinct divisor property’ if τ is injective, that is, if the τ (s) are different for different values of s. We will also say that S has the distinct divisor property if there exists a τ , as above, such that (S, ...
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1. Let P{ή) and p(n) denote the greatest and smallest prime factor of n, respectively. Recently in several papers, Balog, Erdόs, Maier, Sarkozy, and Stewart have studied problems of the following type: if A\,...,Ak are "dense" sets of positive integers, then what can be said about the arithmetical properties of the sums a\ H h % with a,\ G A\,...,ak G Akl In particular, Balog and Sarkόzy proved...
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The height of a polynomial with integer coefficients is the largest coefficient in absolute value. Many papers have been written on the subject of bounding heights of cyclotomic polynomials. One result, due to H. Maier, gives a best possible upper bound of nψ(n) for almost all n, where ψ(n) is any function that approaches infinity as n → ∞. We will discuss the related problem of bounding the ma...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2004
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2004.05.008