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We show that for any prime p≠ 2, ∑ₖ₌₁ᵖ⁻¹(-1)ᵏ k-1 2 k ≡ -∑ₖ₌₁(p-1)/21 k p³ by expressing the left-hand side as a combination of alternating multiple harmonic sums.
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Roberto Tauraso (2010) studied this question.
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