The product of these integers is k! mod p.

Let k=p-1, therefore k! mod p = (p-1)! mod p = -1 mod p.

Therefore (p+1)...(2p-1) = -1 mod p

e.g. 8.9.10.11.12.13 = 1235520 = 176503*7-1 = -1mod7

Jon Perry

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