Perfect Numbers, Cyclotomic Numbers and ABC Conjecture

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  • 完全数,円分数,及びABC予想
  • カンゼンスウ エン ブンスウ オヨビ ABC ヨソウ

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Jenkins recently showed that an odd perfect number must be divisible by a prime greater than 10^7. The aim of this article is to give a new algorithm to obtain such a lower bound. The theory of cyclotomic numbers plays an important role in the algorithm. We also discuss some relation between cyclotomic numbers and ABC conjecture.

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