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x2016+(2016!+1!)x2015+(2015!+2!)x2014+⋯+(1!+2016!)=0x^{2016} + (2016!+1!)x^{2015} + (2015!+2!)x^{2014} + \cdots + (1!+2016!) = 0x2016+(2016!+1!)x2015+(2015!+2!)x2014+⋯+(1!+2016!)=0
Find the number of integer solutions to the equation above.
Notation: !!! is the factorial notation. For example, 8!=1×2×3×⋯×88! = 1\times2\times3\times\cdots\times8 8!=1×2×3×⋯×8.
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