def list_reduced_fractions(d):
count = 1
fractions_list = [(1, d)]
for n in range(2, d):
if common.get_gcd(n, d) == 1:
count += 1
fractions_list.append((n, d))
return (count, fractions_list)
def count_reduced_fractions(max_d):
count = 0
# Even denominators
for d in range(2, max_d+1, 2):
count += 1 # always count 1/d.
for n in range(3, d, 2): # Check only odd numerators
if common.get_gcd(n, d) == 1:
count += 1
# Odd denominators
for d in range(3, max_d+1, 2):
if common.is_prime_mr(d):
count += d - 1
else:
count += 2 # always count 1/d and 2/d for odd d.
for n in range(3, d):
if common.get_gcd(n, d) == 1:
count += 1
return count
