منابع مشابه
On the largest prime factor of the Mersenne numbers
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Recently Hagis and McDaniel have studied the largest prime factor of an odd perfect number. Using their results, we begin the study here of the second largest prime factor. We show it is at least 139. We apply this result to show that any odd perfect number not divisible by eight distinct primes must be divisible by 5 or 7.
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In this paper, we find all integers x such that x − 1 has only prime factors smaller than 100. This gives some interesting numerical corollaries. For example, for any positive integer n we can find the largest positive integer x such that all prime factors of each of x, x + 1, . . . , x+ n are less than 100.
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Let p(n) be the function that counts the number of partitions of n. For a positive integer m, let P (m) be the largest prime factor of m. Here, we show that P (p(n)) tends to infinity when n tends to infinity through some set of asymptotic density 1. In fact, we show that the inequality P (p(n)) > log log n holds for almost all positive integers n. This improves a result of the second author fr...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2014
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2013.12.018