Improving the Chen and Chen Result for Odd Perfect Numbers
نویسندگان
چکیده
If qα is the Euler factor of an odd perfect number N, then we prove that its so-called index σ(N/qα) � qα ≥ 32 × 5× 7 = 315. It follows that for any odd perfect number, the ratio of the non-Euler part to the Euler part is greater than 32 × 5× 7/2.
منابع مشابه
A New Method for Encryption of Color Images based on Combination of Chaotic Systems
This paper presents a new method for encryption of color images based on a combination of chaotic systems, which makes the image encryption more efficient and robust. The proposed algorithm generated three series of data, ranged between 0 and 255, using a chaotic Chen system. Another Chen system was then started with different initial values, which were converted to three series of numbers from...
متن کاملSecurity Analysis of Lightweight Authentication Scheme with Key Agreement using Wireless Sensor Network for Agricultural Monitoring System
Wireless sensor networks have many applications in the real world and have been developed in various environments. But the limitations of these networks, including the limitations on the energy and processing power of the sensors, have posed many challenges to researchers. One of the major challenges is the security of these networks, and in particular the issue of authentication in the wireles...
متن کاملOn generalized fuzzy numbers
This paper first improves Chen and Hsieh’s definition of generalized fuzzy numbers, which makes it the generalization of definition of fuzzy numbers. Secondly, in terms of the generalized fuzzy numbers set, we introduce two different kinds of orders and arithmetic operations and metrics based on the λ-cutting sets or generalized λ-cutting sets, so that the generalized fuzzy numbers are integrat...
متن کاملA Study on the Necessary Conditions for Odd Perfect Numbers
A collection of all of the known necessary conditions for an odd perfect number to exist, along with brief descriptions as to how these were discovered. This was done in order to facilitate those who would like to further pursue the necessary conditions for odd perfect numbers, or those who are searching for odd perfect numbers themselves. All past research into odd perfect numbers has been col...
متن کاملNecessary Conditions For the Non-existence of Odd Perfect Numbers
We start with a result showing most odd cubes cannot be perfect numbers (see Theorem 1). Then we give a new proof of a special case of a result of Iannucci (see [IAN]) that shows that none of the even exponents in N ’s prime factorization can be congruent to 4 (mod 5) if 3|N (Theorem 2). We then extend that result by proving that certain sets of small primes, when taken to a large power, cannot...
متن کامل