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where q1 < q2 < ... < qn. The following table shows that least prime p for which there is a solition:q1! = q2! = ... = qn! mod p
For more information see Unsolved Problems in Number Theory, 1st edition, problem A15. FYI: The 1st edition is no longer in print, but the 2nd edition is available.n p q1 q2 q3 q4 q5 q6 q7 q8 q9 q10 q11 1 2 0 2 2 0 1 3 5 0 1 3 4 17 0 1 5 11 5 17 0 1 5 11 15 6 23 0 1 4 8 11 21 7 71 8 10 20 52 62 64 71 8 599 29 51 123 184 251 290 501 540 9 599 29 51 123 184 251 290 501 540 556 10 3011 0 1 611 723 749 805 2205 2261 2287 2399 11 3011 0 1 611 723 749 805 2205 2261 2287 2399 3009