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Formula:8260

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Digital Library of Mathematical Functions ID 24.15.E10

2 ⁢ n - 1 4 ⁢ n ⁢ p 2 ⁢ B 2 ⁢ n ≡ S ⁡ ( p + 2 ⁢ n , p - 1 ) ( mod p 3 ) , modular-equivalence 2 𝑛 1 4 𝑛 superscript 𝑝 2 Bernoulli-number-B 2 𝑛 annotated Stirling-number-second-kind-S 𝑝 2 𝑛 𝑝 1 pmod superscript 𝑝 3 {\displaystyle{\displaystyle\frac{2n-1}{4n}p^{2}B_{2n}\equiv{S\left(p+2n,p-1% \right)\pmod{p^{3}}},}}


Constraint(s)

2 ≤ 2 ⁢ n ≤ p - 3 2 2 𝑛 𝑝 3 {\displaystyle{\displaystyle 2\leq 2n\leq p-3}}

Symbols List

  • B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}} :
  • S ⁡ ( n , k ) Stirling-number-second-kind-S 𝑛 𝑘 {\displaystyle{\displaystyle S\left(\NVar{n},\NVar{k}\right)}} :
  • ≡ modular-equivalence {\displaystyle{\displaystyle\equiv}} :
  • n 𝑛 {\displaystyle{\displaystyle n}} : integer
  • p 𝑝 {\displaystyle{\displaystyle p}} : prime
  •  Edit this on Wikidata

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This page was last edited on 28 January 2024, at 10:30.
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