def main():
# generics
_time = time()
result = 1
problem = 70
# problem specific variables
_limit = 10**7
_lower = 2
q = _limit
s = 1
r = 0
a = 3
b = 7
# compute answer
while q >= _lower:
p = (a * q - 1) / float(b)
if (p * s > r * q):
s = q
r = p
_lower = float(s) / (a * s - b * r)
q += -1
factor = gcd(r, s)
r /= factor
s /= factor
# output to screen
print r, s
project_euler.__output(_time, problem, r)
return
def main():
# generics
s = time()
result = 1
problem = 70
# problem specific variables
_lower = 2000
_upper = 5000
_limit = 10**7
_primes = project_euler.__eseive(_lower, _upper)
_n = 0
_bn = 1
_phi = 1
_bphi = 0
_ratio = 0
_bratio = float("inf")
# compute answer
for i in xrange(len(_primes)):
for j in xrange(i + 1, len(_primes)):
_n = long(_primes[i] * _primes[j])
if _n > _limit:
break
_phi = long((_primes[i] - 1) * (_primes[j] - 1))
_ratio = float(_n) / _phi
if project_euler.__isperm(_n, _phi) and _bratio > _ratio:
_bn = _n
_bphi = _phi
_bratio = _ratio
# output to screen
project_euler.__output(s, problem, _bn)
print _bratio
return
def main():
# generics
_time = time()
result = 0
problem = 75
# problem specific variables
limit = 1500000
mlimit = int(math.sqrt(limit / 2))
tri = [0 for i in range(limit + 1)]
# compute answer
for m in range(2, mlimit):
for n in range(1, m):
if ((n + m) % 2) == 1 and project_euler.__gcd(n, m) == 1:
a = (m * m) + (n * n)
b = (m * m) - (n * n)
c = 2 * m * n
p = a + b + c
while p < limit:
tri[p] += 1
if tri[p] == 1: result += 1
if tri[p] == 2: result -= 1
p += a + b + c
# output to screen
project_euler.__output(time() - _time, problem, result)
return
def main():
# generics
_time = time()
result = 0
problem = 76
# problem specific variables
total = 100
# compute answer
# output to screen
project_euler.__output(time() - _time, problem, result)
return
def main():
# generics
_time = time()
result = 1
problem = 74
# problem specific variables
limit = 10**6
chains_eq60 = 0
target_chain_length = 60
# compute answer
for i in range(1, limit):
chain_length = fact_loop(i)
if chain_length == target_chain_length:
chains_eq60 += 1
#print(i, chains_eq60)
# output to screen
project_euler.__output(_time, problem, chains_eq60)
return
def main():
# generics
_time = time()
result = 0
problem = 79
# problem specific variables
numbers = set()
keylog = []
# compute answer
f = open(
"C:/Users/Tom/Documents/Projects/Python/Project_Euler/problem_079.txt",
"r")
for char_entry in f:
print(char_entry)
# output to screen
project_euler.__output(time() - _time, problem, result)
return