X value?

[gontajones]

is 4 the only number that has this characteristhic?

Yep.

def chech_num(n):
    if n**n == n + n:
        return 'Ok!'
    else:
        return 'Fail!'


n = float(input('Number: ')) / 2
print(chech_num(n))

To auto check, you can loop through a range of numbers.