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Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.13/43478
- Consecutive integers with equally many principal divisors
Eggleton, Roger B.;
MacDougall, James A.
- The University of Newcastle. Faculty of Science & Information Technology, School of Mathematical and Physical Sciences
- The Fundamental Theorem of Arithmetic is usually stated in a form emphasizing how primes enter the structure of the positive integers, such as: Every positive integer is the product of a unique finite multiset of primes. Alternatively, the Fundamental Theorem of Arithmetic can be stated in a form that focuses on how maximal prime-powers enter the structure of the positive integers, such as: Every positive integer is the product of a unique finite set of powers of distinct primes. Here, Eggleton and MacDougall classify positive integers by the number of principal divisors they possess, where they define a principal divisor of a positive integer n to be any prime-power divisor psupa |n which is maximal. They found that for every n greater than or less than 1 there are only finitely many runs of size greater than N in Psubn, where N is the product of the first n primes.
- Mathematics Magazine Vol. 81, Issue 4, p. 235-248
- Mathematical Association of America
- Resource Type
- journal article
- Full Text