DLMF:24.10.E4 (Q7510)

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DLMF:24.10.E4
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    Statements

    Defining formula
    ( 1 - p m - 1 ) ⁢ B m m ≡ ( 1 - p n - 1 ) ⁢ B n n ( mod p ℓ + 1 ) , modular-equivalence 1 superscript 𝑝 𝑚 1 Bernoulli-number-B 𝑚 𝑚 annotated 1 superscript 𝑝 𝑛 1 Bernoulli-number-B 𝑛 𝑛 pmod superscript 𝑝 ℓ 1 {\displaystyle{\displaystyle(1-p^{m-1})\frac{B_{m}}{m}\equiv(1-p^{n-1})\frac{B% _{n}}{n}\pmod{p^{\ell+1}},}}
    0 references
    DLMF id
    DLMF:24.10.E4
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    Symbols used
    Q11109
    Defining formula
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1acdec
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    Q12121
    Defining formula
    ≡ modular-equivalence {\displaystyle{\displaystyle\equiv}}
    xml-id
    introduction.Sx4.p2.t1.r10.m10abdec
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    Q12122
    Defining formula
    ℓ ℓ {\displaystyle{\displaystyle\ell}}
    xml-id
    C24.S1.XMD3.m1adec
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    Q12115
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C24.S1.XMD4.m1adec
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    Q12110
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1cdec
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    Q12117
    Defining formula
    p 𝑝 {\displaystyle{\displaystyle p}}
    xml-id
    C24.S1.XMD8.m1cdec
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