Problem 3 Show that the equation x2⋅(x−1)2⋅(x−2)2⋅...⋅(x−1008)2⋅(x−1009)2=cx^2 \cdot (x - 1)^2 \cdot (x - 2)^2 \cdot ... \cdot (x - 1008)^2 \cdot (x- 1009)^2 = cx2⋅(x−1)2⋅(x−2)2⋅...⋅(x−1008)2⋅(x−1009)2=c has 202020202020 real solutions, provided 0<c<(1009⋅1007⋅...⋅3⋅1)4220200 < c <\frac{(1009 \cdot1007 \cdot ... \cdot 3\cdot 1)^4}{2^{2020}}0<c<22020(1009⋅1007⋅...⋅3⋅1)4 .