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A refinement of the Hamme-Mortenson congruence
the Hamme-Mortenson congruence math
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2010/11/15
Let $p$ be an odd prime. In 2008 E. Mortenson proved van Hamme's following conjecture: $$\sum_{k=0}^{(p-1)/2}(4k+1)\binom(-1/2,k)^3=(-1)^{(p-1)/2}p (mod p^3).$$ In this paper we show further that $$\s...