def generate_count(rmax): counter = 0 mmax = int(rmax*8/(3**0.5)) for m in range(1,mmax): for n in range(1,m/2+1): if gcd(m,n) > 1: continue a = m**2 - n**2 b = 2*m*n - n**2 c = m**2 - m*n + n**2 if a==b: continue else: k = gcd(a,gcd(b,c)) r = (3**0.5/(2*k))*n*(m-n) if r<= rmax: bump = int(rmax/r) print m,n,k,bump counter += bump
def generate_primative_60(rmax): for m in range(1,1000): for n in range(1,m): if gcd(m,n) > 1: continue a0 = m**2 - n**2 b0 = 2*m*n - n**2 c0 = m**2 - m*n + n**2 if a0==b0: continue k = gcd(a0,gcd(b0,c0)) a0,b0,c0 = a0/k,b0/k,c0/k for s in range(1,1000): a,b,c = s*a0,s*b0,s*c0 r = s*(3**0.5/(2*k))*n*(m-n) if r<= 100: yield (a,b,c),(m,n,k,s) else: break
def generate_count(rmax): counter = 0 mmax = int(rmax*6/(3**0.5))+2 for m in xrange(3,mmax): if m%1000==0: print m nmax = m/2+1 for n in xrange(1,nmax): if gcd(m,n) > 1: continue k =gcd(m+n,2*m-n) r = (3**0.5/(2*k))*n*(m-n) if r<= rmax: bump = int(rmax/r) counter += bump #print m,n,bump elif r > 3*rmax: break
from fractions import Fraction
import eulertools
output = [((0,1),(1,1))]
Nmax = 10**8
counter = 0
for i in xrange(0,Nmax+1):
temp = []
for lb,ub in output:
md = (lb[0]+ub[0],lb[1]+ub[1])
mp = (lb[0]*ub[1] + ub[0]*lb[1],2*lb[1]*ub[1])
if eulertools.gcd(mp[0],mp[1])!=1:
raise
if md[1] <= Nmax:
if mp[1] <= Nmax:
if 100*mp[0] < mp[1]:
counter += 1
if 100*lb[0] < lb[1]:
temp.append((lb,md))
if 100*md[0] < md[1]:
temp.append((md,ub))
if len(temp) == 0:
break
output = temp
if i% 100000==0:
print i,counter
import eulertools p=1009 q = 3643 n = p*q phi = (p-1)*(q-1) A = [(e,(eulertools.gcd(e-1,p-1)+1)*(eulertools.gcd(e-1,q-1)+1)) for e in range(2,phi) if eulertools.gcd(e,phi)==1 ] minA = min([a[1] for a in A]) print minA print sum([a[0] for a in A if a[1]==minA])
import eulertools
cmax = 10**16
counter = 0
for i in xrange(1, 10**4):
if i % 100 == 0:
print i, counter
for j in range(1, i):
m = i**2 - j**2
n = 2 * i * j
a = abs(m**2 - n**2)
b = 2 * m * n
c = m**2 + n**2
if c > cmax:
break
if eulertools.gcd(a, c) == 1 and eulertools.gcd(b, c) == 1:
area = a * b / 2
if area % 6 == 0 and area % 28 == 0:
pass
else:
counter += 1
print counter
# it looks like all are super perfect
# a^2 + b^2 = c^2 + d^2 = L
# (a+c)(a-c) = (d+b)*(d-b) = L-b^2 - d^2
import eulertools cmax = 10**16 counter = 0 for i in xrange(1,10**4): if i% 100 ==0: print i,counter for j in range(1,i): m = i**2 - j**2 n = 2*i*j a = abs(m**2 - n**2) b = 2*m*n c = m**2 + n **2 if c > cmax: break if eulertools.gcd(a,c)==1 and eulertools.gcd(b,c)==1: area = a*b/2 if area % 6 ==0 and area % 28 ==0: pass else: counter +=1 print counter # it looks like all are super perfect # a^2 + b^2 = c^2 + d^2 = L
import eulertools
import math
r = 105
primitivepoints = {}
for x in range(-r+1,r):
for y in range(-r+1,r):
if x**2 +y**2 < r**2 and (x,y)!= (0,0):
k = abs(eulertools.gcd(x,y))
key = (x/k,y/k)
if key not in primitivepoints:
primitivepoints[key]=0
primitivepoints[key]+=1
N = primitivepoints.values()
a = sum(N)/2
c = sum(n**2 for n in N)/2
b = (a**2 - c)/2
sol = sum([b*n-a*n**2 + n**3 for n in N])/3
print sol