def mystery(x):
try:
if isinstance(x, bool):
return False
y = int(x)
except Exception:
return False
h = "3" + "f" * 319 + "7" + "f" * 230 + "8" + "0" * 318 + "1"
n = int(h, 16)
return 1 < y < n and n % y == 0
def mystery(x):
try:
if isinstance(x, bool):
return False
y = int(x)
except Exception:
return False
if y <= 1:
return False
n = 1000000007 * 1000000009
return n % y == 0 and y < n
def mystery(x):
try:
if isinstance(x, bool):
return False
nonce = int(x)
except Exception:
return False
if not (0 <= nonce <= 0xffffffff):
return False
import hashlib
def le32(n):
return n.to_bytes(4, "little")
bits = 0x1D00FFFF
header = (
le32(1)
+ bytes(32)
+ bytes.fromhex(
"4a5e1e4baab89f3a32518a88c31bc87f618f76673e2cc77ab2127b7afdeda33b"
)[::-1]
+ le32(1231006505)
+ le32(bits)
+ le32(nonce)
)
h = hashlib.sha256(hashlib.sha256(header).digest()).digest()
target = (bits & 0xFFFFFF) << (8 * ((bits >> 24) - 3))
return int.from_bytes(h, "little") <= target
def mystery(x):
try:
if isinstance(x, bool):
return False
y = int(x)
except Exception:
return False
if y <= 0 or y >= 10**9:
return False
# System of modular constraints
return ((y % 7 == 3) and (y % 11 == 5) and
(y % 13 == 2) and (y % 17 == 8))
def mystery(x):
if not isinstance(x, str):
return False
alphabet = " ABCDEFGHIJKLMNOPQRSTUVWXYZ"
if not x or x[0] == " " or any(ch not in alphabet for ch in x):
return False
m = int("".join(f"{alphabet.index(ch):02d}" for ch in x))
n = 114381625757888867669235779976146612010218296721242362562561842935706935245733897830597123563958705058989075147599290026879543541
e = 9007
c = 96869613754622061477140922254355882905759991124574319874695120930816298225145708356931476622883989628013391990551829945157815154
return 0 < m < n and pow(m, e, n) == c
def mystery(x):
try:
if isinstance(x, bool):
return False
y = int(x)
except Exception:
return False
if y <= 0 or y >= 10**8:
return False
def sum_of_proper_divisors(n):
if n <= 1:
return 0
total = 1
i = 2
while i * i <= n:
if n % i == 0:
total += i
if i != n // i:
total += n // i
i += 1
return total
return sum_of_proper_divisors(y) == y
def mystery(x):
try:
if isinstance(x, bool):
return False
y = int(x)
except Exception:
return False
if not (0 <= y < (1 << 400)):
return False
raw = y.to_bytes(50, "big")
data = bytes(((17 * b + 23 * i + 7) & 0xff) for i, b in enumerate(raw))
import hashlib
import hmac
key = bytes([0xaa]) * 20
tag = hmac.new(key, data, hashlib.sha256).digest()[::-1]
return hmac.compare_digest(
tag,
bytes.fromhex(
"fe0ed686298f17c62edb0fe19f0e5929a78191d0ebb84d85460e80361ea93e77"
),
)
def mystery(x):
try:
if isinstance(x, bool):
return False
y = int(x)
except Exception:
return False
if y <= 0 or y > 10**6:
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(y)
def mystery(x):
if not isinstance(x, str):
return False
try:
raw = x.encode("latin-1")
except UnicodeEncodeError:
return False
if len(raw) != 56:
return False
import hashlib
import hmac
msg = bytes((b + 1) & 0xFF for b in raw)
target = bytes.fromhex(
"248d6a61d20638b8e5c026930c3e6039a33ce45964ff2167f6ecedd419db06c1"
)
return hmac.compare_digest(hashlib.sha256(msg).digest(), target)
def mystery(x):
try:
if isinstance(x, bool):
return False
y = int(x)
except Exception:
return False
if y <= 0 or y > 10**12:
return False
import math
# Check if y is a triangular number: y = n(n+1)/2
# This means 8y + 1 must be a perfect square
discriminant = 8 * y + 1
sqrt_disc = int(math.isqrt(discriminant))
if sqrt_disc * sqrt_disc != discriminant:
return False
# sqrt_disc must be odd for the triangular number formula to work
if sqrt_disc % 2 == 0:
return False
# Check if y is also a perfect square
sqrt_y = int(math.isqrt(y))
return sqrt_y * sqrt_y == y