2020 problem

x*floor(x*floor(x*floor(x))) = 2020
x = 2020/floor(x*floor(x*floor(x))) 

aside notes:
divisor of 2020: {1, 2, 4, 5, 10, 20, 101, 202, 404, 505, 1010, 2020}

positive:
* but x between 6 and 7 (inc. function)
* so floor(x*floor(x*floor(x))) in (2020/7, 2020/6)
* so floor(x*floor(x*floor(x)) in (288, 337)
=> x = 2020/k for k in 288..337

f(2020/300) => 1811, too small
f(2020/290) => 1985, too small
f(2020/288) => 2405, too big
f(2020/289) => 1999, too small

so no positive solutions

negative
* x between -7 and -6
* so floor(x*floor(x*floor(x))) in (-2020/7, -2020/6)
=> x = -2020/k for k in 288..337

f(-2020/288) => 2756 too big
f(-2020/300) => 2134 too big
f(-2020/310) => 1915 too small
f(-2020/305) => 2020 correct
x = -2020/305 = -404/61