def eul44():
"""Find the pair of pentagonal numbers, Pj and Pk, for which their sum and difference are pentagonal
and D = |Pk − Pj| is minimised; what is the value of D?"""
for i in range(2,3000):
n = i * (3 * i - 1) / 2
for j in range(i - 1, 0, -1):
m = j * (3 * j - 1) / 2
if eul.pentagonal(n - m) and eul.pentagonal(n + m):
return int(n-m)
def eul45():
"""Find the next triangle number that is also pentagonal and hexagonal."""
i = 143
while i:
i += 1
hexagonal = i * (2 * i - 1)
if eul.pentagonal(hexagonal):
return hexagonal
