1 and about 27.5247695102145

1 is the obvious solution just by inspection.

But Desmos shows there is a solution between 27 and 28

https://www.desmos.com/calculator/ydj4bcgrdk

The program below, searching values greater than 1, quickly zooms in on the other solution.  When searching between 2 and 100 subdivided into 1000 intervals, it finds a solution that is between 27.48 and 27.578.  Manually fine tuning the hi and lo values to be searched yields the other solution.

I was unable to search negative numbers because apparently the Python gamma function I am using does not accept negative inputs.

-------------------

import math

# lo = 27.524769510214558

# hi = 27.52476951021458

lo = 2

hi = 100

slices = 1000

for n in range(slices+1):

    if n == 0:

        prior = True

    x = lo + n*(hi-lo)/slices

    big20 = x**20

    gama = math.gamma(x+1)

    if big20 > gama:

        notyet = True

    else:

        notyet = False

        if prior == True:

            print(x - (hi-lo)/slices, x)

            break

    prior = notyet