Hello,

I'd do it straightforward, because I don't know any property letting us simplify this...

17!=2.3.4....16.17

(mod 19)

17=-2

16=-3

15=-4

14=-5

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-->

---->

3x6= -1 mod 19

2x9= -1 mod 19

---->

4x5=19+1= 1 mod 19

7x8=56=57-1=3x19-1= -1 mod 19

---->

Now, calculate a in