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Formula:8208

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Digital Library of Mathematical Functions ID 24.10.E9

E 2 ⁢ n ≡ { 0 ( mod p ℓ ) if  ⁢ p ≡ 1 ( mod 4 ) , 2 ( mod p ℓ ) if  ⁢ p ≡ 3 ( mod 4 ) , modular-equivalence Euler-number-E 2 𝑛 cases annotated 0 pmod superscript 𝑝 ℓ modular-equivalence if  𝑝 annotated 1 pmod 4 annotated 2 pmod superscript 𝑝 ℓ modular-equivalence if  𝑝 annotated 3 pmod 4 {\displaystyle{\displaystyle E_{2n}\equiv\begin{cases}0\pmod{p^{\ell}}&\text{% if }p\equiv 1\pmod{4},\\ 2\pmod{p^{\ell}}&\text{if }p\equiv 3\pmod{4},\end{cases}}}


Constraint(s)

Symbols List

  • E n Euler-number-E 𝑛 {\displaystyle{\displaystyle E_{\NVar{n}}}} :
  • ≡ modular-equivalence {\displaystyle{\displaystyle\equiv}} :
  • ℓ ℓ {\displaystyle{\displaystyle\ell}} : integer
  • n 𝑛 {\displaystyle{\displaystyle n}} : integer
  • p 𝑝 {\displaystyle{\displaystyle p}} : prime
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This page was last edited on 28 January 2024, at 10:30.
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