대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제60권4호
  • /
  • Pages.863-872
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  • 2023
  • /
  • 1015-8634(pISSN)
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  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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ON THE GREATEST COMMON DIVISOR OF BINOMIAL COEFFICIENTS

  • Sunben Chiu (School of Mathematical Sciences South China Normal University) ;
  • Pingzhi Yuan (School of Mathematical Sciences South China Normal University) ;
  • Tao Zhou (School of Mathematical Sciences South China Normal University)
  • 투고 : 2022.03.02
  • 심사 : 2023.04.21
  • 발행 : 2023.07.31
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초록

Let n ⩾ 2 be an integer, we denote the smallest integer b such that gcd {(nk) : b < k < n - b} > 1 as b(n). For any prime p, we denote the highest exponent α such that pα | n as vp(n). In this paper, we partially answer a question asked by Hong in 2016. For a composite number n and a prime number p with p | n, let n = ampm + r, 0 ⩽ r < pm, 0 < am < p. Then we have $$v_p\(\text{gcd}\{\(n\\k\)\;:\;b(n)1\}\)=\{\array{1,&&a_m=1\text{ and }r=b(n),\\0,&&\text{otherwise.}}$$

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과제정보

Supported by National Science Foundation of China (No. 12171163).

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