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GH from MO
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The answer is yes, and the proof can be found in V. J. W. Guo, J.-C. Liu, Proof of some conjectures of Z.-W. Sun on the divisibility of certain double sums, Int. J. Number Theory 12 (2016), 615-623.

GH from MO
  • 105.4k
  • 8
  • 293
  • 398