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Formula:8259

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Digital Library of Mathematical Functions ID 24.15.E9

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


Constraint(s)

1 ≀ n ≀ p - 2 1 𝑛 𝑝 2 {\displaystyle{\displaystyle 1\leq n\leq p-2}}

Symbols List

  • B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}} :
  • S ⁑ ( n , k ) Stirling-number-second-kind-S 𝑛 π‘˜ {\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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