def mystery(x):
if not isinstance(x, int) or x <= 1:
return False
def is_happy(n):
seen = set()
while n != 1 and n not in seen:
seen.add(n)
n = sum(int(digit) ** 2 for digit in str(n))
return n == 1
return is_happy(x)
def mystery(x):
if not isinstance(x, int) or x <= 0:
return False
c = 0
r = int(x ** (1.0/3.0)) + 5
for a in range(1, r):
for b in range(a + 1, r):
if a**3 + b**3 == x:
c += 1
return c == 2
def mystery(x):
if not isinstance(x, int) or x <= 1:
return False
# Check if x is a perfect square
sqrt_x = int(x ** 0.5)
if sqrt_x * sqrt_x != x:
return False
# Check if digit sum is 9
digit_sum = sum(int(d) for d in str(x))
return digit_sum == 9
def mystery(x):
if not isinstance(x, int) or x < 1:
return False
k = 0
lim = int(x ** 0.25) + 20
for i in range(1, lim):
for j in range(i + 1, lim):
if i**4 + j**4 == x:
k += 1
return k == 2
def mystery(x):
if not isinstance(x, int) or x <= 0:
return False
sq = x * x
sq_str = str(sq)
for i in range(1, len(sq_str)):
left = int(sq_str[:i])
right = int(sq_str[i:])
if left + right == x and left > 0 and right > 0:
return True
return False
def mystery(x):
if not isinstance(x, int) or x <= 0:
return False
c = 0
r = int(x ** (1.0/3.0)) + 20
for a in range(1, r):
for b in range(a + 1, r):
if a**3 + b**3 == x:
c += 1
return c == 3
def mystery(x):
if not isinstance(x, int) or x <= 0:
return False
# Count divisors efficiently
divisor_count = 0
for i in range(1, int(x**0.5) + 1):
if x % i == 0:
divisor_count += 1
if i != x // i:
divisor_count += 1
# Sum of digits
digit_sum = sum(int(d) for d in str(x))
return divisor_count == digit_sum
def mystery(x):
if not isinstance(x, int) or x <= 0:
return False
c = 0
r = int(x ** (1.0/3.0)) + 30
for a in range(1, r):
for b in range(a + 1, r):
if a**3 + b**3 == x:
c += 1
return c == 4
def mystery(x):
if not isinstance(x, int) or x <= 0:
return False
s = str(x)
for i in range(1, len(s) + 1):
prefix = int(s[:i])
if prefix % i != 0:
return False
return True
def mystery(x):
if not isinstance(x, int) or x <= 0:
return False
c = 0
r = int(x ** 0.5) + 20
for a in range(1, r):
for b in range(a + 1, r):
if a**2 + b**2 == x:
c += 1
return c == 3