Each of x, y and z is a positive integer with gcd(x,y,z)=1
Determine all possible pairs (x,y,z) satisfying this equation:
x3+y3=7z3
where x+y+z < 10^10
I did not check all the way to 10^10 for the sum of x+y+z.
Checking for x,y < 10,000 I found only one solution
(x,y,z) = (4, 5, 3)
64 + 125 = 189 = 7*27 = 7*3^3
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big = 10000
for x in (range(big)):
for y in range(x,big):
zcubed = (x**3 + y**3)/7
if zcubed%1 != 0:
continue
if not iscube(zcubed):
continue
z = round(zcubed**(1/3))
if x+y+z > 10**10:
print('too big', x,y,z)
if gcdList([x,y,z]) != 1:
continue
print(x,y,z)
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Posted by Larry
on 2024-04-13 13:17:07 |
a solution
