def naive(n):
cnt = 0
for i in xrange(1,n+1):
for j in xrange(i,n+1):
for k in xrange(j,n+1):
a = (i+j)**2 + k**2
b = (i+k)**2 + j**2
c = (j+k)**2 + i**2
x = min(a,b,c)
if euler.isSquare(x):
cnt += 1
return cnt
f = convergent(seq)
f = f.cancel()
h = f.num
k = f.den
#print seq,f
if h*h - v0*k*k == 1:
return h,k
i += 1
assert(i < 100)
#print continuedFraction(decimal.Decimal(61).sqrt())
#print getCF( decimal.Decimal(61).sqrt(), 22 )
lst = []
for i in range(1001):
if not euler.isSquare(i):
x,y = pell(i)
print i,'-',x,'/',y
lst.append((x,i))
print lst[max( range(len(lst)), key = lambda i : lst[i][0] )][1]
#print pell(61)
#maxv = 24
#seq = getCF( decimal.Decimal(61).sqrt() , maxv )
#print seq
#for i in range(1,maxv):
# f = convergent(seq[:i])
# h = f.num
# k = f.den
for i in xrange(1,n+1):
for j in xrange(i,n+1):
for k in xrange(j,n+1):
a = (i+j)**2 + k**2
b = (i+k)**2 + j**2
c = (j+k)**2 + i**2
x = min(a,b,c)
if euler.isSquare(x):
cnt += 1
return cnt
assert( naive(99) == 1975 )
assert( naive(100) == 2060 )
for i in xrange(1, 50):
print i, naive(i)
def take(n, iterable):
"Return first n items of the iterable as a list"
return list(itertools.islice(iterable, n))
def squares():
for i in itertools.count(1):
yield i**2
for s in [7225]:
#for s in take(220, squares()):
for u in itertools.takewhile(lambda x : x < s, squares()):
v = s - u
if euler.isSquare(v):
print s, math.sqrt(u), math.sqrt(v)/2
