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(129) 4

Part of 1986 Tournament Of Towns

Problems(1)

TOT 129 1986 Autumn S4 1987 /( 1 986 !! + 1985 !! )

Source:

8/29/2019
We define N!!N !! to be N(N−2)(N−4)...5⋅3⋅1N(N - 2)(N -4)...5 \cdot 3 \cdot 1 if NN is odd and N(N−2)(N−4)...6⋅4⋅2N(N -2)(N -4)... 6\cdot 4\cdot 2 if NN is even . For example, 8!!=8⋅6⋅4⋅28 !! = 8 \cdot 6\cdot 4\cdot 2 , and 9!!=9v7⋅5⋅3⋅19 !! = 9v 7 \cdot 5\cdot 3 \cdot 1 . Prove that 1986!!+1985!!1986 !! + 1985 !! i s divisible by 19871987.
(V.V . Proizvolov , Moscow)
factorialnumber theoryDividedivisibledivisor