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Chitsai Liu's user avatar
Chitsai Liu's user avatar
Chitsai Liu
  • Member for 14 years, 7 months
  • Last seen more than 2 years ago
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asked
Is the following identity true?
awarded
 Nice Question
revised
A combinatorial identity involving harmonic numbers
added 18 characters in body
revised
A combinatorial identity involving harmonic numbers
added 18 characters in body
asked
A combinatorial identity involving harmonic numbers
accepted
Integer Polynomial solutions to functional equation
asked
Integer Polynomial solutions to functional equation
accepted
A combinatorial identity involving generalized harmonic numbers
awarded
 Nice Question
awarded
 Yearling
revised
A combinatorial identity involving generalized harmonic numbers
edited tags
revised
Prove $4\sum_{k=1}^{p-1}\frac{(-1)^k}{k^2}\equiv 3\sum_{k=1}^{p-1}\frac{1}{k^2}\pmod{p^2}$
deleted 77 characters in body
awarded
 Nice Question
accepted
Prove $4\sum_{k=1}^{p-1}\frac{(-1)^k}{k^2}\equiv 3\sum_{k=1}^{p-1}\frac{1}{k^2}\pmod{p^2}$
revised
Prove $4\sum_{k=1}^{p-1}\frac{(-1)^k}{k^2}\equiv 3\sum_{k=1}^{p-1}\frac{1}{k^2}\pmod{p^2}$
added 4 characters in body
revised
Prove $4\sum_{k=1}^{p-1}\frac{(-1)^k}{k^2}\equiv 3\sum_{k=1}^{p-1}\frac{1}{k^2}\pmod{p^2}$
added 257 characters in body
comment
Prove $4\sum_{k=1}^{p-1}\frac{(-1)^k}{k^2}\equiv 3\sum_{k=1}^{p-1}\frac{1}{k^2}\pmod{p^2}$
@ tkr, I have checked your congruence mod $p^3$ for $p\ge 7$ and find it is true, which I didn't notice. Thanks!
revised
Prove $4\sum_{k=1}^{p-1}\frac{(-1)^k}{k^2}\equiv 3\sum_{k=1}^{p-1}\frac{1}{k^2}\pmod{p^2}$
added 362 characters in body
awarded
 Curious
awarded
 Critic