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NO-ABEL 2018 Problem 1

    For an odd number n, we write n!!=n⋅(n−2)...3⋅1n!! = n\cdot (n-2)...3 \cdot 1 . How many different residues modulo 10001000 do you get from n!!n!! for n=1,3,5,…n= 1, 3, 5, … ?

    Dataset text AI-MO AoPS. Quoted with source.

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