def problem142(): i = 1 record = 7691793 while True: a1 = i**2 # we need a1 - a3 = a6 > 0 for j in range(2,i): a3 = j**2 if isSquare(a1 - a3): # a6 is positive a6 = a1 - a3 # need now that a3 and a4 have the same parity as a4 + a3 = 2x for k in range(j%2,j,2): a4 = k**2 a5 = a1 - a4 a2 = a3 - a5 if a2 > 0 and a5> 0 and isSquare(a5) and isSquare(a2): if (a1 + a2) % 2 == 0 and (a5 + a6) % 2 == 0 and (a3 - a4) % 2 == 0: x = (a1 + a2)//2 y = (a5 + a6)//2 z = (a3 - a4)//2 if x + y + z < record and x > y and y > z and z>0 and all([isSquare(x-y), isSquare(x+y), isSquare(x+z), isSquare(x-z), isSquare(y+z), isSquare(y-z)]): return x + y + z i += 1 print(i)
def dictionariesGivingSquares(word): dictionaries = [] for dictionary in possibleDictionaries(word): numb = numberReplacement(word,dictionary) if isSquare(numb): dictionaries.append(dictionary) return dictionaries
def problem80(): getcontext().prec = 102 total = 0 for a in range(2, 100): if not isSquare(a): b = Decimal(a).sqrt() #total += applyToDigits(int(b * 10**100), lambda x: x) total += sum(int(c) for c in str(b * 10**100)[:100]) return total
def solveQuadratic(a,b,c): disc = b**2 - 4*a*c soln = [] if disc > 0: if isSquare(disc): d = integerSquare(disc) if (-b - d) % (2*a) == 0: soln.append((-b - d) // (2*a)) if (-b + d) % (2*a) == 0: soln.append((-b + d) // (2*a)) return soln
def problem141(): #GOAL = 10**12 GOAL = 10**12 # 623708737 = 10**9 total = 0 for a in range(2,int(GOAL**(1/3))): for b in [r for r in range(1,a) if (a**3*r + r**2 < GOAL and gcd(a,r) == 1)]: e,n = 1,0 while n < GOAL: n = a**3*b*e**2 + e*b**2 if isSquare(n): print(a,b,e) total += n e += 1 return total
def problem211():
total = 0
for n in range(1, 64 * 10 ** 6):
if isSquare(sigma(n, 2)):
total += n
return total