Question
$$n(n-1)(n-2)(n-3)(n-4) = 1000000$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} n(n-1)(n-2)(n-3)(n-4) &= 1000000&& \text{simplify left side} \\[1 em](1n^2-n)(n-2)(n-3)(n-4) &= 1000000&& \\[1 em](1n^3-2n^2-n^2+2n)(n-3)(n-4) &= 1000000&& \\[1 em](1n^3-3n^2+2n)(n-3)(n-4) &= 1000000&& \\[1 em](1n^4-3n^3-3n^3+9n^2+2n^2-6n)(n-4) &= 1000000&& \\[1 em](1n^4-6n^3+11n^2-6n)(n-4) &= 1000000&& \\[1 em]n^5-10n^4+35n^3-50n^2+24n &= 1000000&& \text{move all terms to the left hand side } \\[1 em]n^5-10n^4+35n^3-50n^2+24n-1000000 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using Newton method.
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Polynomial Equations Solver