On the Greatest Common Divisor of Binomial Coefficients

@article{McTague2017OnTG,
  title={On the Greatest Common Divisor of Binomial Coefficients},
  author={Carl S. McTague},
  journal={The American Mathematical Monthly},
  year={2017},
  volume={124},
  pages={353 - 356}
}
  • Carl S. McTague
  • Published 2017
  • Mathematics
  • The American Mathematical Monthly
  • Abstract Every binomial coefficient aficionado1 knows that the greatest common divisor of the binomial coefficients equals p if n = pi for some i > 0 and equals 1 otherwise. It is less well known that the greatest common divisor of the binomial coefficients equals (a certain power of 2 times) the product of all odd primes p such that 2n = pi pj for some 0 ≤ i ≤ j. This note gives a concise proof of a tidy generalization of these facts. 

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