On the Success of Mishandling Euclid's Lemma

@article{Dudek2016OnTS,
  title={On the Success of Mishandling Euclid's Lemma},
  author={A. Dudek},
  journal={The American Mathematical Monthly},
  year={2016},
  volume={123},
  pages={924 - 927}
}
  • A. Dudek
  • Published 2016
  • Mathematics
  • The American Mathematical Monthly
Abstract We examine Euclid's lemma that if p is a prime number such that p |ab, then p divides at least one of a or b. Specifically, we consider the common misapplication of this lemma to numbers that are not prime, as is often made by undergraduate students. We show that a randomly chosen implication of the form r|ab ⇒ or r|b is almost surely false in a probabilistic sense, and we quantify this with a corresponding asymptotic formula. 
2 Citations
On the Success of Seriously Mishandling Euclid’s Lemma
A summation involving the number of divisors function and the GCD function
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