def nroot(x,n):
    lo = 1
    hi = x//n
    while lo <= hi:
        mi = (lo+hi)//2
        test = mi**n
        if test < x:
            lo = mi + 1
        elif test > x:
            hi = mi - 1
        else:
            return mi
    return lo

b = 2
fac = 2
while True:
    prod = b+1
    i = b+1
    while prod < fac:
        i += 1
        prod *= i
    if prod == fac:
        print("%s! = %s! %s!"%(i,b,b))
    for N in range(2,i-b):
        j = nroot(fac,N)
        prod = 1
        for k in range(j,j-N,-1):
            prod *= k
        while prod < fac:
            j += 1
            prod //= j-N
            prod *= j
        while prod > fac:
            prod //= j
            prod *= j-N
            j -= 1
        if prod == fac:
            print("%s! = %s! %s!"%(j,j-N,b))
    if b % 10 == 0:
        print("  %s"%b)
    b += 1
    fac *= b